I'm not sure what your getting at here. In the second picture it looks fine. The lenses on these are adjustable so it doesn't matter if it's sticking out a bit.
Sometimes the threads in the top part of the module are not cut fully to the bottom and that could mean a lens doesn't screw all the way in. Sometimes the focus ring thread isn't cut all the way so it too doesn't screw on as far as others. If your laser focuses to infinity with this situation then don't worry at all. If you've not fitted your diode yet, make sure it is pressed beyond flush to give you the most adjustment of focus possible. Often, the problem with focusing Blurays comes down to this. You will need to find some tool, (do a search for, "inexpensive diode press tool", or have a hunt for tools sold by members here specially for the job), to do this but it's not difficult. Using the back end of the Aixiz module as a press tool will only get you to a flush fit.
(You'll also probably be best to put some teflon plumber's tape on the threads to make sure you have a nice tight focus adjustment. The metal lens assemblies can be a little loose fitting. This is also considered normal.)
I can't see what you mean too clearly, but If you can remove it, great. If not, then you'll only know if it's a problem when you have a diode installed. In normal operation, however, the lens would stick out further than this if it's an Aixiz, 3 element, glass lens coated for 405nm so I really wouldn't worry.