No, Jesus was not 'more strict than the Pharisees on this issue'.
You have missed His point - His various points - in his answers to the Pharisees' questions.
We've been round the words several times already, on this and other threads, and so I'll not engage you further here. Except to cite the verses, in case anyone else wishes to contemplate their true meaning:- Matthew chapter 19 verse 1 to verse 12.