The surge light monitors the MOV to make sure that it is still able to divert power surges away from connected equipment. When the surge light is on, the surge protector is offering surge protection.
If the surge light is off, this means that the surge protector has either received a powerful enough electrical surge (s) that it damaged the MOV inside or that normal fluctuations in electricity that cause minor power surges and have caused the MOV to wear out.
In either case, if connected equipment is NOT damaged, this is not considered a claim or warranty issue. The surge protector took the "damage" from the power surge (s) and protected connected equipment. However, the surge protector will no longer offer surge protection and should be replaced if the "surge light" has gone out.