I'm really not a fan of saddle soap, etc.... on my strops as the results can be unpredictable. Maybe an application of Neat's Foot Oil would renew it but I can't promise anything.

I would try a very light coating. Put a little into the palm of you hand, rub it with the other hand to disperse it a bit then rub the strop with both hands. This method will apply very small amounts evenly where just painting or pouring it on will cause it to sink in unevenly and possibly leaving way too much.

Tony