Wall is a good example of an established ruling on this type of scenario.
AFAIK (and according to ORCID), JT is a restrict, not a protect. The same logic can still apply, but I can see both sides better.
JT (Ability):
No opponent may remove a card from holder's draw pile. Draw pile may still be searched and/or shuffled.
JT (Play-As):
Restrict opponents from removing cards from your deck.