I've only worn old long sleeve t-shirts a few times with the intention of not getting them back....

• tossed one under an aid station table at mile five of a marathon (gone). 
• dropped one on a pile of other throwaways outside the starting corral of a HM (gone).
• flung one over a guardrail outside the starting corral of a HM and retrieved it after the race.

If I wear gloves, I wear them for the entire race.

For small local races, I've dropped stuff on the ground before races and picked it up afterwards.