An old school-friend of Dagwood's turns up to visit and seems to spend most of his time making rude remarks about the furniture and the food etc. Blondie stays silent out of politeness but later that evening she lets Dagwood know that he owes her a big favour in return. The remark "You owe me one" often means, "I've just done you a favour and at some time in the future you can pay me back". I suppose the look of surprise on Dagwood's face suggests that he doesn't realise how difficult the visit has been for Blondie.
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