So, there's going to be a lot of different reply's to this. Anywhere from throw it out to it's fine for non-critical use.
My opinion is it's fine for non-critical use, e.g. tying up a boat, etc. Even though it's not suitable any more for the extreme use of fall prevention it still has plenty of strength for not so extreme use.
My next question is, how often does everyone replace their throw-bag ropes?
REI suggests replacing climbing ropes every 1 to 5 years (depending on use)
(Climbing Rope Care
Another study shows that dirty ropes can loose up to 40% of their strength
(A new study tests the strength of soiled climbing ropes | Climbing
I replace my climbing rope every 5 years (I'm not a very active of a climber)
but I know people who have had the same throw-rope for more than that.
How often do you replace your throw-rope?