Blue Tits returning to nesting box

Hi.  We have taken great delight in watching two blue tit parents working tirelessly over the past couple of weeks, feeding their chicks in our nesting box.  Of late, we could hear the chicks very clearly each time a parent bird took food in.  Today, it is clear that the chicks have fledged as there is minimal traffic now but.......... At intervals of about 2 hours or so, the parent(s) has returned with food in the mouth and gripped onto the front of the box, putting just it's head inside.  I think it may be trying to encourage a remaining chick to come up to the hole and fledge.  Eventually, they do go inside but I can't hear any noise.  My questions are:  is it likely that this is the parent(s) trying to save a final (perhaps weaker) chick?  And also, what is best for us to do?  I could easily take the box down and hand feed any remaining chick by hand until I can get it to our local bird rescue lady, but am loathe to do that in case this is traumatic to the parent(s).  Can anyone offer any advice - because if there is something I could be doing, I really do want to help.  Maybe it's best to let nature take it's course?