Replace. Some say that filter media is meant to be washed and reused, but my experience is it passes ginormous amounts of dirt.
If it were up to me, I would throw that away and install 2" pleated MERV 7 (or 8) disposable pleated filters. I usually purchase these from a local supply house that specializes in air filters because they will often sell any size needed for a reasonable price. The prepackaged media available in hardware stores can be okay in a pinch, but they are often a poor value and those stores usually do not sell anything thicker than 1" pleated.
A 2" pleated Merv 7 Filter looks something like this:
Actual width and height are typically 1/2 inch under nominal. Actual thickness is typically 1/4" under nominal. (16 x 20 x 2 nominal is actually 15.5 x 19.5 x 1.75 to give installation clearance). Air filter supply houses specializing in this media can usually fabricate these to order at a reasonable price. These are called "pleated air filters, MERV 7 (or MERV 8)." The MERV rating refers to the particle size that the filter traps. Higher number gives tighter filtration, but most residential blowers cannot tolerate a filter more restrictive than MERV 8.