Mr Gove visited Trump Tower in New York as part of a part-time job he has with The Times newspaper and posed for a grinning thumbs-up picture with Mr Trump.
The Tory MP for Surrey Heath was left facing accusations he failed to grill Mr Trump on controversial issues.
Questions were also asked over whether he should be allowed to leave parliament to do paid work outside of politics.
He came up against Wakefield Labour MP Ms Creagh on the BBC’s Daily Politics show.
She told Mr Gove: “Nothing mentioned in your interview questions his comments on women, which I find disgraceful.
“I think that creates real questions about this second job that you’ve got.”
Mr Gove said: “Well I think that people will form their own judgements about the appropriateness of politicians writing.”
Ms Creagh then interrupted: “And thumbs upping.”
The parliamentary register of financial interests shows that Mr Gove writes a weekly column and other articles on request for The Times.
The register says: “Expected remuneration of £150,000 a year from News UK, 1 London Bridge Street, London SE1 9GF, in return for an average of 8 hrs per week.”