Carole Radziwill got into it with Sai De Silva while they filmed the upcoming season of "The Real Housewives of New York" ... and it's all because Carole was dragged into the Jeffrey Epstein mess.

Production sources tell TMZ ... Sai made it a point to bring up Carole's name being in the infamous Epstein Files.

Carole was close to Epstein associate Ghislaine Maxwell.

Carole addressed her ties to Ghislaine in an interview with The New York Times back in March, saying ... "Imagine knowing someone… and then they turn out to be, like, a monster."

Ghislaine is also the photographer who snapped Carole's author photo for her 2005 memoir. 

Sources tell TMZ Sai and Carole beefed throughout the season … after Sai decided to grill Carole about the Epstein Files … telling people she felt the need to speak up because she has children. 

Sources tell TMZ the season wrapped, but the cast is still finishing filming confessionals. 

A production source tells TMZ ... 'RHONY' producers were delighted with Carole … after deciding to bring her back to the show for season 16. Carole previously starred on the show from seasons 5 to 10. 

We're told Carole is featured in every episode despite being a friend of the cast. The producers felt Carole really delivered during production.

A production source tells TMZ ... Carole was asked to be a full-time cast member but declined … because she doesn't want the obligations.