Is it permissible for him to go for ‘umrah when there is an unsettled dispute between him and his friend?

Firstly: 

It
is not permissible for a Muslim to shun his brother for more than three
days, and the better of them is the one who is first to reconcile and
forgive. Imam Ahmad (15824) narrated from Hishaam ibn ‘Aamir that he said:
The Messenger of Allah (blessings and peace of Allah be upon him) said: “It
is not permissible for a Muslim to shun a fellow Muslim for more than three
days, for they are both in the wrong so long as they are shunning one
another. Whichever of them is the first one to (take the initiative and)
seek reconciliation, his taking the initiative will be an expiation for him.
If he greets him first and the other one does not accept (his initiative)
and respond to his greeting, the angels will respond to him and the Shaytaan
will respond to the other one. And if they die without resolving their
dispute, neither of them will ever enter Paradise.”

Classed as saheeh by al-Albaani in Saheeh at-Targheeb (2759) 

Secondly: 

The differences and arguments that usually arise between partners or friends
cannot be resolved by fighting and cutting off ties; rather they are to be
resolved through the intervention of good people who strive to reconcile
between them and restore rights to those to whom they belong. Allah, may He
be exalted, says (interpretation of the meaning):

“There is no
good in most of their secret talks save (in) him who orders Sadaqah (charity
in Allah’s Cause), or Ma‘roof (Islamic Monotheism and all the good and
righteous deeds which Allah has ordained), or conciliation between mankind,
and he who does this, seeking the good Pleasure of Allah, We shall give him
a great reward”

[an-Nisa’ 4:114]. 

If
it becomes clear that one of them is the transgressor and wrongdoer, and is
persisting in that, and the other one cannot take back his rights from him,
then the one who is in the right has the choice between forgiving him – and
forgiving him is preferable – or claiming redress for that wrong on the Day
of Judgement. 

But it is not permissible to sever ties between them for more than three
days under any circumstances. 

At
the very least one of them must greet the other with salaam if they meet,
because the greeting puts an end to shunning and avoids incurring the burden
of sin. Please see the answer to question no. 98636 

Thirdly: 

If
you are the one who was wronged, you should try to resolve the dispute that
occurred between you and your friend before you go for ‘umrah, and you
should ask him to refer the issue to an intermediary to resolve the issue on
the basis of Islamic teachings. If he agrees to that, all well and good,
otherwise the minimum that there should be between you is exchange of
greetings (salaam). 

The scholars of the Standing Committee said: 

What is required of the Muslim, if there is resentment between him and his
brother, is that he should go to him, greet him with salaam, and speak
kindly to him in hopes of bringing about a reconciliation, because in doing
so there is a great deal of reward and avoidance of sin.

End quote from Fataawa al-Lajnah ad-Daa’imah (26/128) 

Muslim (2565) narrated from Abu Hurayrah that the Messenger of Allah
(blessings and peace of Allah be upon him) said: “The gates of Paradise are
opened on Mondays and Thursdays, and every slave who does not associate
anything with Allah is forgiven, except a man between whom and his brother
is some grudge. It is said: Wait for these two until they reconcile, wait
for these two until they reconcile, wait for these two until they
reconcile.” 

Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

That is: the Lord, may He be glorified and exalted, will not look at your
deeds on Mondays and Thursdays if there is a grudge between you and your
brother.

End quote from ash-Sharh al-Mumti‘ (5/206) 

Undoubtedly you want to go for ‘umrah and perform it in the manner
prescribed in Islam, and ask Allah to accept it from you and to forgive you
your sins, but your forsaking your brother and not reconciling with him will
prevent your deeds from being accepted and will bar the way to forgiveness.
So you must hasten to reconcile with him before you go for ‘umrah. 

Ibn ‘Uthaymeen said: 

The individual must hasten to resolve grudges and put an end to enmity and
resentment between him and his brothers, to the extent that even if he sees
in himself some reluctance to try to resolve the issue, and he finds it
burdensome, he must be patient and seek reward with Allah, for the
consequences of doing so will be very good. When a person understands what
there is in an action of goodness and reward, it becomes easy for him, and
if he understands the warning against not doing it, it will become easy for
him to do it. If he is not able to go to that person and say: We have to
reconcile and resolve the enmity and resentment between us, then he can ask
a trustworthy man who is respected by both parties to intervene, and go to
him and say: I see that there is such and such between you and So-and-so; if
you reconcile and resolve the enmity and resentment between you, that will
be a very good thing.

End quote from Sharh Riyadh as-Saaliheen (p. 1828) 

We
give you the glad tidings of the words of the Prophet (blessings and peace
of Allah be upon him): “The better of them is the first to greet the other
with salaam” Narrated by al-Bukhaari (6077) and Muslim (2560). He (blessings
and peace of Allah be upon him) also said: “The one who is closest to Allah
is the one who initiates the greeting of salaam.” Narrated by Abu Dawood
(5197); classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

So
go to him and greet him with salaam, and – in sha Allah – you will be better
than him and closer to Allah then him. Then go for your ‘umrah and ask Allah
to reconcile between you and restore your rights to you. 

If
you do not do that, and you continue shunning him, then you go for ‘umrah,
if you perform it in the manner prescribed, then it will be valid, but there
is the fear that you may miss out on a great deal of goodness or forgiveness
because of shunning a Muslim. The entire matter is subject to the will of
Allah, so strive to attain that which is with Him by obeying Him, may He be
glorified. 

For more information, please see the answers to questions no.
65500 and 93888

And Allah knows best.