I think Grehyton meant the gate necklace, not really a teleport stone.
As for the guard quests (newbie quests), I spent a few hours collecting parts for them with a 60's tracker, and didn't manage to budge my faction level at all (not to mention the parts being frustratingly rare). A few hours isn't really enough to go by, but I would assume the higher level quests given out by Samanth give much bigger faction hits than the newbie quests. I don't know if the newbie quests have a hard cap on how much faction you can gain with them (like the newport quests do).