I don't use anything but an inexpensive solution found in the supermarket:
Multipurpose No Rub Soution (for soft contact lenses) - I use the "LiveBetter" brand but I don't think the brand is important. The "no rub" is.
It's not magic - I have to use it at least twice a day.
Step 1 Wipe the eye area using a dry paper towel using very little to no pressure.
Step 2 Moisten a new towel or apply solution directly to area around eyes
Step 3 Wipe using very little to no pressure; keep going back and forth over discolored area a lot.
My cat produces A LOT OF DISCOLORING TEARS - but as you can see in the pic has little to no staining because I do this constantly.
Unfortunately - If I missed 2 days - she'd look a horrible mess, horrible.
Personally, I don't recommend powders, bleachers, whiteners, etc.....for all the obvious reasons.
Also, I'm not happy with the idea of using antibiotics as a cosmetic (to temporarily halt discoloring eye discharge) - as I'm wary of this kind of intervention. But this is just my opinion - many, many here use Eye Envy or even antibiotics from a Vet.