Hook Removal and Foam Bugs

I was fishing the other day and did pretty well. I did have a problem
spotting my fly on the water with all of the debris on the water. A
fish or two took the hook pretty deep. After trying to remove the
hook a few times (putting the fish back in the water to rest between
attempts) I cut the line near the beetle.

It was a foam beetle. I did not (I forgot) to crimp the barb. My
question is, how long does one try to remove the hook. Will leaving
it in the mouth (including the foam bug) be a problem. I guess the
question comes down to does it matter if the bug you're leaving in the
fishes mouth is foam or a fur and feather.

Thanks in advance.