Not had that problem. But, If I were you I'd pick up a can of compressed air and see if that could get it out, doubt air would hurt the pickup, the steel wool might, but don't quote me on it.
Ofcourse, if you got a high power vacuum that might work wonders, but that's not really household stuff.
The blue-tack might work too, gotta loosen and make it abit more sticky first though I reckon.