How can I block or fill out a letterbox hole in my door?
I don't think that there'll be something you can buy off the shelf for this.

As it might be tricky to find a block of wood the right depth it could be easier to insert a piece of plywood on the each side of the hole so it fits snugly. Fill the gap around the edge, sand and paint. You may find it easier to make the hole a little larger to create a lip to give the plywood something to sit against. If you make it flush and arrange the grain of the plywood to go the same way as the wood of the door it won't be very noticeable. You can fill the void with some insulation.

If you have a block of wood roughly the right size then use that. Any gaps can be filled with wood glue mixed with sawdust to give a "woody" texture.