The interference suggests that the GPS contains a switching power supply which is radiating a lot of muck. Or the GPS itself radiates a lot of muck which is conducted down the cable.
Does that product conform to any emissions specs? It cannot be sold in the EU if it doesn't, but the specs may not mean anything in an aircraft scenario.
I have a satphone car holder which does the same.
Such products should not be sold into the aviation market, though the satphone car holder (a Thuraya product of
Turkish manufacture) would stop VHF radio reception in the car also.
It might be easy to fix or it might not. With the satphone I had to build a filter comprising of two capacitors and a double inductor. A clamp-on ferrite filter is cheap and simple but did nothing at all.