My brake expertise is based on modest personal experience and what I learn elsewhere (books, web, mechanic friends). In other words, don't depend on my advice!
I am not sure how removing the master cylinder cover would affect your current problem.
My understanding of disk brakes (someone correct me) is that there is no return spring to retract the pads/piston and that the shape and design of the piston o ring seals (not protective boot)results in a TINY retraction of the piston.
To me, if your caliper boot is not seated correctly, I would fear that it could impose a TINY amount resistance in the piston movement that MIGHT affect the TINY amount of retraction that is caused by the o ring seals.
Just my understanding of things. But, I would make sure the boot is seated as it was designed.
And yes user52165, thanks for clarifying the need to use a blunt tool to poke around the boot. I had to order a new OEM boot from the dealer once because of impatient use of a screwdriver!