How can you tell if a battery has been damaged by under or overcharging?

The only way is with a load test. Use the same procedure for VRLA DRY CELL batteries that you would use with a flooded cell battery:

1. Recharge if the open circuit voltage is below 75%.
2. If adjustable, set the load at three times the 20-hour
3. Apply the load for 15 seconds. The voltage should stabilize above 9.6 volts while on load.
4. If the battery has a CCA rating, you can apply a load equal to ½ the rating for 15 seconds. The voltage should stabilize above 9.6 volts while on load. To apply a more determined test, you may apply a load equal to 100% of the rated CCA for 30 seconds or a load of 5 to 7 times the AH rating for 30 seconds. The voltage should stabilize above 7.2 volts while on
5. If below 9.6 volts (7.2 volts for the 100% CCA test), recharge and repeat the test. If below 9.6 volts (7.2 volts for the 100% CCA test) a second time, replace the battery.