FWIW.....
After I purchased my truck, I found out that it had a remote start similar to what the OP is talking about. My Wife told me the salesman had informed me it was there but I must not have heard him. I went in for an oil change at my local dealer (not the dealer I had purchased the truck from and during that, they installed some updates to the truck, including the RFH update. After getting the truck back, I found that there were random errors (remote start would not work, doors would not lock/unlock with the keyfob and the TPMS light would come on even though the EVIC showed that the air pressure in all 4 tires was exactly what it was supposed to be). I took the truck back to that dealer and was told the problems were originating in the remote start unit and were not covered by the factory or the extended warranty I had on the truck.
After talking with them some more, I was told to talk to the selling dealership. The selling dealership had me bring the truck in and they investigated the issue. The conclusion came back that the update to the RFH had created a problem with the aftermarket remote start unit and now the truck was getting "strange" signals that it could not interpret. After a few phone calls back and forth, it was decided that the selling dealer would remove the aftermarket remote start and replace it with an OEM unit based on the fact that I purchased a CPO unit and everything on it was supposed to be covered by both the factory warranty and the additional extended warranty.
Bottom line, I would make them remove the aftermarket unit and install the OEM unit if that is what they had agreed to at the time of purchase. Otherwise, you will have them telling you that the warranty on your truck does not cover the aftermarket add on when things go wrong.