If the filter is made from foam on both sides than it should be fine to steep in hot water + washing up liquid. I wouldn't be too pushed though - looks clean enough to me.
yep, its foam on both side. The top is protected by that metal mesh... but I guess a soaking would do it. I'll leave it for a while so if it seems clean enough.
I had a similar panel filter (Trust) in the RX-7 before I swapped in a Blitz SUS set, massage it in a bucket of hot suds and make sure to rinse it well after washing. Let it dry overnight on the radiator and you're sorted.