Paraguad IUD and lena menstrual cup?

I've had my Iud since March and I just got a lena menstrual cup in the small size and I got it in and out okay but I'm just worried about possibly pulling my Iud out.  My strings are trimmed and are always kind of coiled up at the very top of my cervix just to where I can barely feel them.... I checked after I took it out and my strings were there.  Anybody have any tips for inserting and removing it?