@ehBeth,
It's a shame I don't have the context either.
Let's just imagine those 'things' are lovely dogs,
and 'they' are my friends living next door.
Say, I love dogs. Well, I actually do.
And I've always wanted to play with the dogs, but I was too busy.
Then, my friends happen to have a long vacation, and I ask them,
'Well, could I please look after those dogs while you guys are away?'
And they say, 'Yes.' and I jump with joy.
Would the sentence 'As a favor, they want me to look after the dogs.' might make more sense now?
What about this one?
Say, I hate dogs.
Unfortunately, my friends about to go on vacation, ask me to look after those dogs. In this case, I can't say 'As a favor, they wanted me to look after
the dogs,' because I don't like to take care of the animals.
Am I right?
I wish I could explain better what I'd like to ask. Dang.
Anyway, I will be looking forward to seeing your reply.