The Careers use Peeta to figure out what Katniss' skill was that got her the eleven from the Gamekeepers. The Careers also think that Peeta might know Katniss' whereabouts.
Chat with our AI personalities
The careers want to kill Katniss, as they know she's a threat. They realise that to do this they need to know her weaknesses so they use Peeta to try and find out Katniss' weaknesses, they plan to kill Katniss and then kill Peeta and move on.
The Careers use Peeta to figure out what Katniss' skill was that got her the eleven from the Gamekeepers. The Careers also think that Peeta might know Katniss' whereabouts.
They were using him to get to Katniss and then they were planning to kill him.
Peeta loves Katniss for real, and wants to protect her. If the careers knew about Katniss' skills, it would be easier for them to know her weaknesses and/or how to kill her. Peeta wants to keep Katniss alive without getting himself killed.
They want to use him to lead them to Katniss and find out the secret of her high score from him.
Peeta
In the beginning of the games, Peeta joins the careers in order to keep Katniss safe. This way her could lie to them about where he thinks she might be hiding and what her strengths/weaknesses are.