You would pretty much have to be adding enough salt to kill your betta for it to alter any readings. Regardless, I don't personally believe that adding salt regularly serves any purpose, ESPECIALLY if you already have water with a ton of different minerals and stuff in it. It's just not necessary. The only time I use salt is when I'm treating ich.
Even if you do decide to add regularly, a tablespoon is way too much for a 3g tank. I use a tablespoon per 5g when treating ich and that's an elevated dose.
That gH reading makes me question the accuracy of the test kit. You don't get mineral deposits and discoloration with extremely soft water.
Use several strips and compare, do they even have the same readings?
I bought those same strips a few years ago and they never read correctly compared to my liquid kit.