If you are looking for visible evidence that it has healed, it may be hard to see at first. The bark around the wound will swell up and kind of cap itself off, but the wood will still be exposed. When you see the edges of the woond swell up, then, since this is so close to the ground, I would paint the exposed wood with any good quality paint. In fact, I would start with an oil based primer, then a good latex over that.

In the meantime, mix a little boric acid (roach powder) in with some hot water and when it cools, cover the wood with it. This will delay any rot and discourage any insect activity while the wound heals.

Judging by the new information, I don't think this tree is in any immediate danger from this incident.