I don't know about throwing it in a washer. I'm not familiar with landwire mesh. I haven't ever worked with it, maybe someone who has made toys can post the way they clean theirs.
I have a couple of plastic baskets that have weaved fleece strips throughout, and I wash those in dish detergent. They get soaked in hot soapy water, then rinsed well. Occasionally, I will follow with a v/w solution dip or spritz on my girls toys, the larger get spritzed while smaller toys can be dipped, then get followed up with a final rinse.