Does a +1/+1 counter placed on a creature by a triggered ability get removed if the creature leaves and returns to the battlefield?

When a permanent leaves the battlefield and returns, it is treated as an entirely new object with no connection to its previous existence on the battlefield. This is established in CR 400.7, which states that an object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence.

Because of this 'new object' rule, any +1/+1 counters that were placed on the creature before it left the battlefield do not carry over. The counters remain on the card conceptually in the previous zone (usually the graveyard or exile), but since counters are tied to the permanent as it exists on the battlefield, they simply cease to exist when it leaves. The creature returns to the battlefield clean, with no counters.

It is important to distinguish this from effects that say 'return it to the battlefield with' a number of counters — in that case, the counters are placed on the creature as part of the return event, not carried over. CR 121.1 confirms counters are placed on permanents and have no existence independent of them.

Concrete example: Your 2/2 creature has a +1/+1 counter on it, making it a 3/3. Your opponent uses a blink effect (exile it, then return it to the battlefield). The creature re-enters as a 2/2 with no counters — the +1/+1 counter is gone because the returned creature is a brand-new object.