In order to get rid of the fly trap, you need to make sure ALL weeds have been pulled. You should be able to dig it up, or, it should be gone by the next day. If you have to water your flowers, the Fly trap will wilt if not watered. I never tried to see if it would disappear after wilting, so I'm not sure if it will disappear, or if you still need to make sure all weeds are pulled (the grassy looking weeds). Clovers don't count as a weed since they can also be a Lucky clover. I deliberately grew one to have in my town since it takes a lot of weeds and time to get one.
GG loves ACNH!