John Gill Commentary Mark 6:26

"And the king was exceeding sorry; but for the sake of his oaths, and of them that sat at meat, he would not reject her." — Mark 6:26 (ASV)

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.