Expensive gifts aren't enough to make Kyle Richards forgive and forget.

When Kim, 46, presents her sister with a custom-made bracelet the morning after a heated NYC dinner exchange with Camille Grammer, Kyle has a difficult time expressing her gratitude.

"As much as I wanted to just move forward and have a nice lunch, I could not get myself to look at her," Kyle, 41, says.

Kyle explains that Kim should have had her back when she began arguing with Grammer the night before, but "for some reason my sister didn't want to step up to the plate and say, 'I was there and Kyle never said that.'"

Counters Kim: "I couldn't get a word in!"

The Real Housewives of Beverly Hills airs Thursday at 10 p.m. (EST) on Bravo.