No, it's not a charisma check either. It's a reaction check (less than friendly), which is a combination of party reputation and the speaker's charisma.
Charisma needed at various reputation levels:
Rep 20: CHA <= 12
Rep 18-19: CHA <= 13
Rep 16-17: CHA <= 14
Rep 14-15: CHA <= 15
Rep 8-13: CHA <= 17
Rep 5-7: CHA <= 18
Rep 4: CHA <= 19
Rep 3: CHA <= 20
Rep 2: CHA <= 21
Rep 1: CHA <= 22
Of course, if you want a friendly reaction (as with basically all other NPC interactions that care), you negate these; rep 20 needs charisma >= 13 for a friendly reaction, for example.
Yes. Good example also is Jared who requires Reaction 15 to give the boots. I had charisma 17 and reputation 13 and it was not enough. I didn't get the boots this time.
Comments
Charisma needed at various reputation levels:
Rep 20: CHA <= 12
Rep 18-19: CHA <= 13
Rep 16-17: CHA <= 14
Rep 14-15: CHA <= 15
Rep 8-13: CHA <= 17
Rep 5-7: CHA <= 18
Rep 4: CHA <= 19
Rep 3: CHA <= 20
Rep 2: CHA <= 21
Rep 1: CHA <= 22
Of course, if you want a friendly reaction (as with basically all other NPC interactions that care), you negate these; rep 20 needs charisma >= 13 for a friendly reaction, for example.