The first fledglings for the chickadees have left the nest. I recommend that you take the old nest and toss it into your compost bin. Once you clean out the birdhouse of the old nest you have a good chance of a 2nd nesting.
This gives me a great chance to show you the materials that a chickadee uses to build it’s nest. This bird builds a soft nest by starting with some mossy material, add in pine straw for structure, and finish the inside with a soft downy material such as animal hair or feathers.