Walter wouldn't voluntarily have asked the Klopeks to pick up his mail. That's a given. He shat himself when he saw them. They'd be the last he'd ask.
So, they obviously waited till Walter had left to go to the hospital then gone round and stole it.
That's a point...how come with all the snooping and prying did Walter sneak away without anyone hearing or seeing anything.
TIMELINE
Okay, it was the night Ray, Art and Mark were spying on Hans knocking the crap out of his garbage can. So Walter must have gone between 11-11:30pm (the rainstorm after Ray and Art had gone home) and when the garbies arrived. Which was early, cos even military-disciplined Rummy was still half-dressed and shaving.
So, the Klopeks must've gone round to Walters in the dead of night. Is that why the place had signs of a struggle? They basically trashed the place, taking his toupee, mail etc...
Interesting...