What is the ruling on saying, “May the angels of the Most Gracious say Bismillah over you”?

Firstly:

The angels

The angels are honoured slaves of Allah who have the characteristics that Allah has mentioned in His book (interpretation of the meaning):

{[All] praise is [due] to Allah, Creator of the heavens and the earth, [who] made the angels messengers having wings, two or three or four. He increases in creation what He wills. Indeed, Allah is over all things competent} [Fatir 35:1]

{The heavens almost break from above them, and the angels exalt [ Allah ] with praise of their Lord and ask forgiveness for those on earth. Unquestionably, it is Allah who is the Forgiving, the Merciful} [ash-Shura 42:5].

Secondly:

Was it narrated that the angels say Bismillah over anyone?

There is no report in the Islamic texts to suggest that the angels say Bismillah over anyone; rather it was narrated that they pray for forgiveness for the believer . So if someone says: “May the angels pray for forgiveness for you,” and the like, that is more appropriate and is better.

But we say: there is nothing wrong with such phrases that are commonly used by people, because saying Bismillah is no more than a kind of dhikr (remembrance of Allah), and the intended meaning is: May Allah protect you; or it is a supplication asking Allah to protect and take care of the other person. There is nothing wrong with any of that. The angels glorify and remember Allah, and among the angels are guardians and protectors who protect people by Allah’s command and decree, as Allah, may He be exalted, says (interpretation of the meaning):

{For each one are successive [angels] before and behind him who protect him by the decree of Allah. Indeed, Allah will not change the condition of a people until they change what is in themselves. And when Allah intends for a people ill, there is no repelling it. And there is not for them besides Him any patron} [Ar-Ra‘d 13:11].

In other words, Allah has angels who come in succession to protect His slave from all directions, coming one after another without any delay. Each of them comes straight after the other, taking turns to protect him by night and by day from all harm that could touch him or anything bad that could happen to him. This protection is by the command of Allah, meaning because Allah has commanded them to do that. And when the decree of Allah [for some harm to befall him] comes to pass, the angels forsake him."(At-Tafsir al-Wasit  5/416).

Moreover, if someone were to say: “May the angels of the Most Gracious say Bismillah over you,” he is not saying that this is what the angels do; rather it is a supplication asking that the angels might say Bismillah over him, and is a prayer for protection for him, asking that the blessing of Allah’s name be bestowed upon him. This is clearly a good intention, and there is nothing wrong with it, in sha Allah.

Conclusion:

There does not seem to be anything wrong with this phrase, and there is nothing to dictate that one should be strict about it or tell off anyone who says it.

And Allah knows best.