The only solution is probably to advocate for moving away from "REST" entirely—for all parties. Mend the discord by coining two new terms and clearly articulate the two meanings that should be attached to them.
("Indian" is another word like this, but that did not get fully deprecated. This is resulted in lots of confusion. "'Indian'? Like Native Americans?" "No, Indian as in 'from India'" "Oh, all right." A similar thing is happening with "open source".)
This probably involves making the terms (or at least one of them—so long as it's the right one) somewhat cool. Maybe the non-REST term should be AROH (pronounced like "arrow") for "Application RPC Over HTTP".