This is what happens:

She hears the alarm, and leaves Aran'gar and Delana to see what the fuss is about. She has Ramshalan brought to her in a separate room, and immediately wrapped him up in air and "dug into his mind", making him spill the beans. She opens a gateway, considering fleeing, but then Aran'gar comes along. She asks if Delana knows compulsion, and sends for her, then sends for the dove. She puts the weave on the dove, then Delana returns and performs the compulsion.

So lazy doesn't seem to be the reason, as she was already using Compulsion to make him talk, and she sent for Delana before doing the thing with the dove, so that's not it either.

She knew Rand, or rather Nynaeve, would be able to detect, and possibly read or remove, the Compulsion, but there is no hint that she thinks they might be able to figure out who placed it there.