Originally Posted by PaperPrincess

I think what you are saying is that the feet in the walking foot are grabbing the jersey & pilling the fabric?
I would try putting a piece of giftwrap tissue paper over the fabric & try quilting thru that. You should still be able to see the design on the shirt & then just tear it off when you are done.
You can also try lessening your presser foot pressure (check your manual).
Finally, use scraps from the offending shirts to perfect the technique.