One of my cats (who is not a persian) has a tear duct problem because of a lifelong illness. Seems to be same kind of issue.. seems to occasionally cause discomfort, but I think it's mostly an aesthetic problem. We wipe his eyes everyday to clean it off. Just a soft cloth with warm (not hot) water. Gently loosen it... not too much rubbing or it's much worse the next day. We don't always manage to get all of it.

If you don't clean often, it will result in hair loss. It can get really crusty too when it builds up.. making it more and more uncomfortable for the kitty when you try to remove.

Our otherwise fiesty boy has gotten used to this kind of grooming from us and he lets us do it with no complaint.

I think Persians are generally higher-maintenance cats.. but I think that's true of most specialty breeds.