As Thief of Blood enters the battlefield, remove all counters from all permanents. Thief of Blood enters the battlefield with a +1/+1 counter on it for each counter removed this way.
Experience counters aren’t removed from players this way, but loyalty counters are removed from planeswalkers.
If more than one Thief of Blood enters the battlefield at the same time, you can apply the replacement effect of any of them. That one will enter with additional +1/+1 counters due to its own ability and the others will not.