Zim, although definitely seeing Tak as a nuisance, does not seem to take her seriously. Even after she plants explosives in his base and becomes a major threat to his "mission", he fails to see the damage she can really do. When he learns of her plan through MiMi's memory disc, he merely states that "her little joke has gone far enough". However, he finds that getting rid of her is harder than it seems, and he ends up needing Dib and Gaz to defeat her. During their final battle outside Earth's atmosphere, Tak attempts to explain that his mission on Earth was a lie, told by the Tallest to get rid of him. In the end as he makes a report to the Tallest, and Zim brushes Tak's explanation off as "lies".
Early on in Tak, The Hideous New Girl, Zim doesn't recognise Tak as another Irken, but thinks that she is a human girl who has fallen in love with him (a conclusion he draws when he misinterprets her gift of Valentine's meat as a token of affection, rather than her making an attempt to blend in, and cause him pain to boot).
Interestingly, Zim chooses to take this opportunity to learn more about the nature of human affection, and attempts repeatedly to win her "affection" - with each attempt leading to suffering on his part. It is debatable whether or not Zim himself has developed a crush on Tak, or whether it's his ego that leads him to fancy the idea she loves him. However, the latter idea is the more likely. The writers never establish Zim's feelings towards Tak, although it is clear that she hates him. However, even knowing Tak doesn't really love him, Zim tries everything humanly possible to get her to love him.
Had the series gone continued, Tak would have reappeared, making her a recurring villain trying to get in Zim's way. In Top of the Line, she would have entered a competition among the other Invaders, during which their SIR Units would be put through a series of tests (not unlike a dog show). Tak's role would have been to sabotage the other SIRs, leaving all but MiMi, Skoodge and Tenn´s SIR Units and GIR destroyed. Because the script was never recovered, her interaction with Zim during the course of the episode is to be determined.
After her appearance in Tak, The Hideous New Girl, her voice appears in Backseat Drivers From Beyond the Stars and Dibship Rising through her crashed ship, which has her personality downloaded into it. Zim recognizes her ship during both encounters he has with it, although he makes no comment on her or how Dib got the ship.