Do birds remove egg shells from the nest once they have hatched?

I found half of a house sparrow egg shell in my garden yesterday. It seems evident from the way it had broken that the chick hatched naturally, as opposed to having been predated. I do have a pair of house sparrows nesting in a nestbox on my outside wall, and the the chicks must have hatched very recently because I have seen both parents going in and out frequently for the past day or two with insects in their beaks. I was just wondering if it's likely that the egg shell I found was from this nest? It was about 20 feet away from the nestbox, under a bush. This is the only pair I know that are nesting anywhere near. Would the parents remove the shells once they are empty? Or would it be more likely that this shell fell out of another nearby nest that I do not know about/found its way into my garden by other means?

 

I know I'm not really explaining myself very eloquently (I have a headache and it's very very humid here today!!), so I hope this makes sense!