i'm not inclined to re-use the filters. they were not very expensive. you can buy a steel mesh replacement for the paper filters and just use that over and over. i find the ability to just pop out the grounds and the filter into the compost with no muss and fuss to be a positive.
You can reuse filters perhaps once or twice. It is very easy to make your own filters by cutting out your own filters from a #2 size drip filter and it's relatively cheap. I can get four aero press filters out of one #2 size drip filter. Gives you lots of options to choose from as there are lots of makers of #2 size filters.