Tatterkite

If Tatterkite would enter with counters on it, it enters but doesn't have those counters. For example, if an effect grants it persist and then it's destroyed, it returns to the battlefield without a -1/-1 counter on it.

Tatterkite's ability prevents any kind of counter from being placed on it, not just -1/-1 counters.

A spell or ability whose effect would put a counter on Tatterkite simply doesn't affect it. The spell or ability isn't countered. If it would put counters on any other creatures, it continues to do so.