Reputation in Fallout 2 is a way to measure general feeling for your character in each of the towns you visit. Reputation can be modified by doing good or bad deeds, like completing quests or killing townsfolk.
FOnline has alot of stuff based on Fallout 1 & 2, I think they use exactly same reputation system as Fallout 2.
That's what I know, maybe you should join IRC www.forestnet.org channel: #2238 and ask a Game master, they should know.
But I'm pretty sure the information I provided is correct. It depends however, FOnline may have a different reputation system.
From what i remember, Fallout 2's reputation with factions only had a title, rather than any numbers.
Whereas Karma, had both numbers and a title.
So you could say its a modified Karma system.
. Is there something I can do to get back in their good grace or I'm just going to have to live with it?
Trade things to the merchants that they don't usualy trade in.
E.G Weapons to the doctor, or Healing Powder to Buster.