Why not make it more consistent with a: If that enchantment was an aura or the artifact was an equipment, you may...?

I looked at that. The wording actually seemed smoother this way, and I feel like the flavor works slightly better this way; I destroy something parasitic and add something to a creature. Otherwise I can destroy an equipment that is NOT in use and still get a counter, which wasn't as mush what I was looking for.

Could this be expanded to say: If that artifact/enchantment was attached to a permanent?

Absolutely. It had been that, but it looks like I needed it while rewriting it.

Small thing, but that's the wrong "its."

I know, it challenges Naturalize pretty hard when I make the same card -. In this environment though, its most frequent targets will net the “victim” some life. Going this way allows me to make a somewhat flashy common that has situational relevance within the set.

What if this was called 'Restoration'? Disengage works but there's the +3 life part that doesn't quite jibe. Whereas restoring something implies bringing it back to its true nature (something green wants to do) as well as making it as shiny as new (the +3 life).

Honestly, I don't really understand why this isn't just Nature's Claim. Yes, this wording allows you to emphasize the importance of aura and equipment in the set, but I don't know there needs to be a better Nature's Claim just for the sake of flavor.