You don't see them much on golf courses because they have greenkeepers working all the time, but they can be a problem even there in shadier, damper spots; they certainly don't use chemicals to kill earthworms, they're illegal. They sometimes use abrasive top dressings to discourage earthworms, but these topdressings applied twice yearly often damage the turf and its roots, which means they need to repair or replace it regularly. Presumably, though, you're not growing sports turf, don't have a greenkeeper handy every day, and don't keep it so short either. I can't say I blame your wife for not wanting to rake the grass before she walks on it, and it would serve no useful purpose if the casts weren't dry anyway. You might consider putting in a path or judicially placed stepping stones for her to use, which would at least avoid the casts being squashed and smeared across the grass whilst wet, though it won't solve the problem of smearing when you use the mower.

Can't you just spray it with the garden hose? It's mud! It will wash away like nothing. The worms are what help keep your lawn vibrant green & healthy looking. They aerate the soil, improve soil structure, add nutrients improve water retention, etc.

Also you sure are asking for trouble asking your wife to rake the lawn before hanging out the laundry!

As it appears to be you who wants rid, had you thought of raking it yourself when the washing is nearly ready for hanging out?

I've just thought of another solution - have artificial turf laid instead. Done professionally, and having made a good choice of all the types available, it'll look great year round, with never a worm cast in sight. The only drawback is how hot it gets in high summer in full sun.