I believe you get 10 guardian favor every 12 hours, which is kind of silly because the cap is 1000 points. Quoted from the lodestone:
You will gradually earn “favor” with your Guardian (10 every twelve Eorzea hours up to a maximum of 1000). When this has reached a certain amount, you can petition the god or goddess to bless you with a temporary boost to the development rate of various skills.
I have been in groups, and most people seem to be intent on finishing the leve as fast as possible. In fact, most people don't even pick up guardians favor, leaving whoever initiated the leve to get it. One group I had earlier was down to one dodo left on the leve. I suggested we grind some since we had 20 minutes left. No one really seemed to be up for.
This is really disappointing, as I have found doing leves in large groups to be pretty lackluster in the XP department. The only time I've actually found it worth it is if you're doing the leve well below the leve level (i.e I had a group of lvl 5s doing lvl 10 leves, and it was loads of fun, whereas a group of lvl 10s doing lvl 10 leves is a boring spam fest).