Yes he knows thay Ha-ri is Geum-hee but he doesn't know the specifics.
However, Ha-ri's fake identity, but thankfully not her employment status, is soon exposed after the real Jin Young-seo gets into a parking accident with Cha Sung-hoon , Tae-moo's secretary, who was acting as Tae-moo's driver at that moment.
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Korea JoongAng Daily in Korean.
Without the ability to fly, they mutually agree that he will be just as extinct as his namesake if he tries to jump down.
The wily grandpa surely knows because he knew Ha-ri's fake name that Tae-mu used Ha-ri as a fake girlfriend to get out of blind dates.