Depends on what system you are using.
This is my take when someone asked earlier this week what the difference was between banishing and cleansing,
Yes they’re using it in the transitional Solomonic sense of “giving license to depart” which means letting the entity go and do the work. It doesn’t mean getting rid of it as I use it: but then, I do not use the Solomonic system.
I have used it in this sense as per the instructions in Corwin Hargrove’s Jinn Magic, in which you complete the ritual by blowing out the candle and sensing the beings going on their way to do the work.
Then I would say the banishing didn’t work. As the entity was invited, I would not be too worried about this, but I would ask it why it wasn’t leaving. Maybe there was more to do and it was trying to tell you something.
Well maybe YOU’RE not, but I would caution against assuming everybody else is automatically doing the same thing, given we are all using different systems from many different teachers, unless you ask someone specifically you just won’t know.
Personally, I don’t typically banish an invited entity, but if I intend to banish, I’m attacking that entity as an uninvited parasite, an enemy, and that thing is gone, gone, and possibly dead.
Why not? There’s nothing wrong with your using it that way if that’s what works for you.