Mark 6:26

And the king was exceeding sorry
(See Gill on Matthew 14:9)

yet for his oath's sake, [and] for their sakes which sat with him;
as Matthew adds, "at meat", ( Matthew 14:9 ) ; for it seems as if supper was not over, when all this was transacting.

He would not reject her;
deny her her request, or send her away without granting it which could not be without grieving her, and treating her with contempt, and defrauding her of the promise; all which ideas are expressed by some versions.