Remember that Grima was a Man of Rohan, not a cartoon gnome like movie-Grima. Anyway, Grima was extremely sly. He apparently poisoned Theoden remember? I'm sure he would resort to such devilry if he wanted to do the deed with Eowyn.
I don't think he'd ever pluck up the courage to do it though.
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Los Ingobernables de Harlond
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