Hundred percent that's a pipe insert that has become jammed in the fitting. Make a concerted effort to unscrew the collar around it and the entire fitting will come apart, screw collar, slide washer, rubber seal, toothed ring, ring release collar etc will all fall out along with the pipe insert and you'll see (reassemble in same order to reuse). The toothed ring tends to drag the insert out of the end of the pipe when withdrawing the pipe from the tee
If it's metal, be aware that some push fit pipe companies, like Hep2O, do have metal inserts.
Be wary of mixing brands; use the same brand of insert and pipe, as the outer diameter of the insert matching to the inner diameter of the pipe is the important bit where cross brand variance comes in. Most pipe should be compatible outer diameter for cross brand use of fittings, unless brand X's too-large-for-brand-Y's-pipe has been used, swelling the OD of the brand Y pipe
Or do you think it will be okay as is?
If you got it fully fitted (did you cut the pipe on its printed markings and insert so far as to get to the next marking?) it will probably be ok; the only concern I have with such relates to how the cut end of the pipe interacts with the seals.
The normal process I follow for push fit (JG) is:
Cut the pipe square on one of the * markers
Run a Stanley knife round the inner diameter to put a slight chamfer on the edge
Push a superseal insert in; the chamfer helps avoid the pipe destroying the seal on the stem of the insert
The end of the pipe now has a chamfer on the outer edge thanks to the insert
The whole lot goes into a JG fitting all the way up to the next * on the pipe and the locking collar tightened
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When doing what you've done it would be wise to put a slight chamfer on both the inner and the outer edges of the pipe, because it is the cut end of the pipe itself that must slide past the main seal in the fitting without damaging it.
When a pipe end is cut square it is very easy for it to pinch the seal against the fitting and cut a lump out of it, leading to leaks
All in with the two step process (insert into pipe, pipe into fitting) you can more easily see if you've nipped a seal
It will only take a few seconds to dismantle the joint if you're concerned, and check the seal (fully unscrew the collar; it will be tough but apply force)