Yep, that's dirty. Clean would be white.
I think that the problem is not as much that the filter is dirty and clogged as it is that the filter is dirty and now dirt is getting past it. The thermal modules have very fine fins on them and once those get coated with dirt, there will be much less heat transfer than there is supposed to be.
You can run the seat for a few minutes without the filter to see if it makes a difference. If it works better without the filter, then you just need a new filter. If it doesn't, then you need a new filter and you need to clean the modules (or the duct to the seat back is loose and leaking).