On all my Ford's, if a check engine light is on, it will not remote start. Just gives a single honk instead of starting. My 2011 Mustang did it after I changed the exhaust and before I got the tuner to turn off the rear O2 sensors. As soon as I got the tuner, I installed the intake, cleared the codes and remote start worked again. My 2015 Explorer Sport this happen three different times and each time, the CEL was on.
Back a few months ago, my new 2017 F250 had one of the batteries crack due to a manufacturers defect. It lost charge and only the passenger side battery was working. Remote start still worked although the push button start wouldn't work most of the time until I got it to Ford.
Hopefully, it's something easy. Even being tuned and deleted, the issue would technically have to be caused by the tune or the deletes for them not to fix it. They could, if they're jerks, void your power train warranty though.