304L contains chromium and what you are seeing is chromium oxide. We used to utilize this for a non-stick surface in brazing jigs by heating the SS jig parts in an evacuated oven and then purging the hot parts with air. The whole SS jig part would become covered with this green oxide. When the jig part was then used to hold other parts together in a brazing bell jar, the oxide layer on the surface would prevent the brazing from sticking to the jig!
So, in your welds, the chromium is oxidizing on the surface. You can heat it again with a reduction atmosphere containing a rich hydrogen content and the oxide will disappear and the shiny SS will return.