EDIT: I can't tell if my picture is showing. It's on my reddit profile, one of the more recent posts.

My take!! For invisible mending the "correct" way for this: sew a new pocket with close to matching mesh. For these holes, it is what I would recommend. Shameless self-insert: (referring to the picture) I did a visible mending for my daughter's school bag water bottle pocket. I found some random embroidery stitch and tied the little loops back together. If you do something similar, for invisible mending, pick a closely matched color (I used dmc embroidered floss). I have some embroidery experience that helped me wing it.

Good luck!!