Deity of Scars's ability causes it to have more toughness when you activate the ability (as a result of losing a -1/-1 counter) and then puts a regeneration shield on it when the ability resolves. If you activate the ability in advance of Deity of Scars being dealt 5 damage, for example, Deity of Scars will be 6/6 before the damage is dealt to it. It won't use the regeneration shield unless it's dealt more damage that turn.

Removing a -1/-1 counter from Deity of Scars is a cost of activating its activated ability. You can't activate the ability if there are no -1/-1 counters on Deity of Scars.

You can pay and remove a -1/-1 counter to activate the ability any time you want. Deity of Scars doesn't need to be in danger of being destroyed.