It sounds like your client didn't use a fusible stabilizer but one where she simply backed the T and sewed around the edges. I have never done a T-shirt quilt done without fusible stabilizer.
Definitely contact your client now, before going any further and ask how she wants you to proceed. You don't have too many options at this point. If she used a non fusible stabilizer as I suspect, you could try using a lot of spray on starch. It would really slow down your quilting process though as you would need to spray starch then let that dry then quilt and repeat this for every advance. But the starch may just stabilize the T's enough to stop the shifting.
You could also try and remove the quilt from your rack, pick out what you have done so far, then cut away all stabilizer on the backs then starch the dickens out of it, let it air dry, press with a pressing cloth and reload, This would be a ton of work though and I would certainly charge extra for all this. And at this point I am guessing as I have never been faced with this issue and can't even say for sure if it would help. I am thinking she probably used a tricot as a stabilizer on the back as that is super slippery and will shift and slip around a lot. Not only against the T but also on the batting.
Oh, one other thing you can try, I don't know if you are working from the back of the quilt with a panto or the front doing freehand quilting. If from the front you can try laying some bolts of fabric or bags of rice on the quilt to create drag and weight. This may help stop the quilt from bouncing around and shifting so much from the hopping foot.
Please come back and let us know what resolution you had. Your experience could help someone else down the line.