Legends: It reports to a guard
According to the New Essential Guide to Droids, TT-8Ls aren't typically tasked with opening doors, and can even be remotely controlled by a guard:
The TT-8L is little more than an eye on a stalk. It remains in a fixed position for its operational life, usually installed near a doorway or inside a lobby. An approaching visitor's footfalls trigger the unit's audio sensors, whereupon it scans the newcomer, compares physical parameters against its internal database, and announces the guest's arrival to its master, who can either admit the visitor or request further observation.
Because the droid's unremarkable intelligence matrix wasn't always enough to please the truly distrustful, Serv-O-Droid installed a remote-activation subroutine allowing the Y7 to be controlled directly by a security guard at any time.
(source: The New Essential Guide to Droids (2006), page 187, emphasis added)
This is reinforced by C-3PO's reaction in the film to the droid retracting into the door after a brief conversation:
"I don't think they're going to let us in, Artoo."
(source: Return of the Jedi)
This implies that he thinks that someone besides just the door droid has made the decision not to admit him and R2-D2.
The Complete Star Wars Encyclopedia confirms that it was Bib Fortuna who typically opened the door:
Tattletale's job, as with all others of its model, was to interview visitors and determine their intentions before deciding whether or not to let them inside. No one got into Jabba's palace without first encountering Tattletale. After a short interview, the droid withdrew into the armored door and informed Jabba's majordomo, Bib Fortuna, that Jabba had guests. Fortuna responded in his own time, of course, and more than one legitimate visitor died of heat exhaustion waiting for the door to open.
(source: The Complete Star Wars Encyclopedia (2008), Volume III P-Z, page 267, emphasis added)
(Note that in the Canon novelization scene that inspired this question, in which Luke mind-tricks his way in through the TT-8L, these details still being true would have odd implications, including Bib somehow being mind-tricked through the droid's report, and also needing to be mind-tricked twice in a row to allow Luke entry. It's unclear which if any of the above details is still true within Canon.)