Eomer sees him eyeing Eowyn from across the room, and it infuriates him that Grima dares to look at her so.

He longs to kill Grima, for this and other reasons- he and Theodred have discussed it many times, both drunk and sober.

But neither are willing to spill blood in the Golden Hall.

There is nothing that can be done. Grima is too close to Theoden; his uncle is too caught in the Worm’s snare. They do not know what the repercussions might be to the King, if Grima were dead.

But Eomer’s patience is fast reaching its threshold.