Remember that you are NOT actually connecting anything to "THE MAINS". You are connecting to the green-wire safety ground.
If your location is new enough to have a GFCI, then it is probably safe to assume that the mains receptacles are likely wired properly with green-wire ground.
Go out and get an ordinary (3-prong) NEMA 5-15 plug and use a green-color single wire to connect the round GROUND PIN to your anti-static mat through a 1M resistor. Leave the flat HOT and NEUTRAL pins floating (connected to nothing). Then you don't have to fool around with the screws on the decorative plate which very well may NOT be grounded, especially if the receptacle is in a plastic box.
If your location is older construction and the GFCI was an "after-market" addition, then it may NOT be safe to assume that the power recptacles are properly grounded. More research and details are necessary to determine whether you have a real ground connection available.
The problem with leaving the "anti-static" mat "floating" is that it will charge up to whatever highest voltage it last came into contact with, and it may take minutes, hours, or days to drain down to zero. An "anti-static" mat that has a residual charge on it is WORSE than no mat at all. It has the capacity of delivering a static discharge all by itself, and it gives a false sense of security.
You did not reveal any details of the location, surroundings, etc. If you are nearby METAL water pipes, then you could connect your mat to those as a surrogate "ground". Of course, plastic pipes are useless for grounding. And gas pluming should NEVER be used for grounding (for what is hopefully obvious reasons!) Or, if you are near an outside wall, etc. you could possibly sink your own ground rod, etc.