It would be very wrong to make other people aware that someone has HIV+
It's quite obvious that people are scared of aids.
Anyway as long as you dont take the blood of the mats and then stick it inside yourself you should be alright. :-P
Infact I don't worry about this, and sometimes when I help close up at night I clean blood, infact I cleaned blood tonight, and I never wore gloves, I just wached my hands when I was done. If the blood was still wet and my hands were cut then i'd probably wear gloves while cleaning it.