After some search on my sources this is what I've found. I still haven't tested any of these: try on small hidden portions of leather, let dry and check the result before applying on the whole surface.
1 - more Water!
Wet evenly the whole surface, let it dry away from sun or other heat sources, then recondition with glycerine soap.
2 - Alchool / Acetone
Friction the stain, let it dry and recondition.
3 - Oxalic acid
A product used for polishing marble, in wood treatment and beekeeping. Be careful, it's pretty toxic... but it's known to work well for this purpose. Dissolve 1-2 table spoon in 1 liter of water, wet evenly the saddle and let it dry. It will slightly lighten leather color but will not damage it.