GPS Patch Antenna Feed Pin PCB Layout
You could treat the feed pin and surrounding copper like a short piece of coax. Coax has a characteristic impedance defined by its inner and outer diameters: -



It's not going to be a million miles wrong given fringing effects - no more than double for what a real piece of coax is but is it really a big issue - your PCB is 0.8 mm thick and there are rules of thumb about mismatches and the same rule of thumb is pretty useful in many scenarios: -

For instance, if the length of a piece of wire is less than one-tenth the wave length of a signal then it's probably not worth worrying so, at 0.8  mm long is this realistically going to pose a severe problem for a frequency less than 1.5 GHz - at this frequency the wavelength is 200 mm.