His grandfather left a bequest to his heirs who are poor; is it permissible for him to take from that bequest?

It is not permissible for a Muslim to bequeath more than
one third of his wealth or to bequeath any of his wealth to his heirs.
This has been explained in the answer to questions number
111918 and
111917. 

Based on that, your grandfather’s bequest is not valid, apart
from what he bequeathed to the Haram, which should be executed with regard
to one third only. 

As for the second third that was bequeathed to the Haram and
the third that he bequeathed to his heirs who are poor, these bequests are
not valid and should not be executed except with the permission of the other
heirs. 

Al-Nawawi said: The scholars of our time are unanimously
agreed that if a person has an heir, his will should not be executed with
regard to more than one third, except with the permission of the heirs. And
they are unanimously agreed that with the heirs’ permission, his will may be
executed with regard to all of the wealth.

End quote from Sharh Saheeh Muslim, 11/77 

Ibn Qudaamah said: To sum up: if a person leaves a bequest to
his heir for which the other heirs did not give permission, it is not valid
and there is no difference of opinion among the scholars concerning this.
Ibn al-Mundhir and Ibn ‘Abd al-Barr said: The scholars are unanimously
agreed on this, and there are reports from the Messenger of Allah (blessings
and peace of Allah be upon him) to that effect.

End quote from al-Mughni (6/449) 

If some of the heirs agreed to the bequest that is more than
one third or the bequest to an heir, but some others do not agree, then in
this case the bequest should be executed with regard to the proportion of
heirs who agreed to it only. 

If the heirs or some of them agree to the bequest of your
grandfather to his heirs who are in need and are poor, then it is
permissible to you to take some of it if you are poor and in need. 

If a person is working but his income is not sufficient to
meet his essential needs, then he is regarded as poor. But if his salary is
sufficient, then it is not permissible for him to take from it. 

Shaykh al-Islam Ibn Taymiyah said: Everyone who does not have
enough to suffice himself and his dependents is one of the poor and needy.
End quote from Majmoo‘ al-Fataawa, 28/570. 

Shaykh Ibn Baaz said: If a person has an income that is
sufficient for food, drink, clothing and accommodation, from a waqf or
earnings or employment and the like, then he cannot be called poor or needy.
End quote from Fataawa Ibn Baaz, 14/266 

And Allah knows best.