Is that the round filter that sit's in the tank at the back. Instead of the kind that hang over the back. If it is i have one in a 10 gallon and i have watched my bettas let it suck them up against it. The would sit there a little while and then swim off without torn fin's. Once he got used to the current then he was fine.
I had all that set up when i first got into bettas. Knowing what i no now, i dont think i would do it. Just because the expenseve bettas i have. But I have done it without any damage.
here is the filter i was using and i think we are talking about..