That is not how orbital mechanics work. It may seem counterintuitive, but if something in orbit gets a push that isn’t strong enough to make it totally escape

That is not how orbital mechanics work. It may seem counterintuitive, but if something in orbit gets a push that isn’t strong enough to make it totally escape orbit, it will stay in a new elliptical orbit. That new orbit will pass through the point where the push happened, so it will come back through that location again, just with a different speed and direction.