I wanted to see how you clean your TRX?

A cleaner & brush?

Throwing it in the washer?

Mine is getting dirty around the handles and is due for some sort of cleaning!

I would say that a little soapy water and a brush would work well; the washing machine might be a little too rough and I can see the straps getting all wrapped up and tangled.  You probably want to make sure that you lay it out and let it fully dry before coiling it or it could start to get kind of funky.