H*ll no.
No. Not at all. Takeout/Pickup should be 0% tacked on or added. That's sort of the whole point of you picking it up.
Happened to me twice recently. Once at Gruit, where they made a whole scene as if they were doing me a favor by removing it. They also had a cr@ppy POS system (is POS a pun?) where they couldn't figure out how to remove the gratuity the system had automatically added to my tab.
Then it happened to me at the newly opened Izzy's fried chicken, it was $3 and I didn't want another scene, so I just paid it.
Glad to hear I'm not crazy. If you're going to charge me the same $$ for taking my food to go, where you don't have to serve me or have me take up a table, at very least have the decency of not forcing the "gratuity" on me.