From what I've seen, it's mountains without your Exploitation — that is, the tiles immediately adjacent to your districts.  This means mountains innate output becomes 3prod/1inf, but I think the 1inf can be exploited by any district?

Exploiting a mountain gets you 1 influence. It's pretty mediocre. Exploitation occurs on all the hexes adjacent to your city's districts / havens / land-built-wonders.