Coal Tits in Nesting Box

Hi all,

We've had a nesting box on a garden wall for about 4 years and this is the first year it's being used, looks like by Coal Tits - they were slightly reticent at first but now we consistently see one or two flying straight into the box (sometimes with food) on a regular basis. There is also some nesting material hanging out of the hole. 

Typically,  this is the year we've given the go ahead for some hard landscaping to start and the wall on which the box is situated is due to be demolished. This is due to take place late June/ early July but obviously we don't want to disturb the nest. From what I've read, it's likely that any eggs would have hatched by then but I wanted to ask whether anyone could offer any advice or thoughts please.

Many thanks!