From what Tak has revealed about her own personality, she can be described as vindictive and bitter, and capable of holding quite the grudge for a very long time. This is best illustrated by her relentlessness in tracking Zim down to punish him for ruining her chances of becoming an Invader 50 years ago. She even went so far as to follow him to Earth and set up her own base of operations in order to steal his mission, and get the honor she thinks she deserves from the Almighty Tallest.
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 recognize Tak as another Irken, but thinks that she is a normal human girl who has fallen in love with him (a conclusion he draws when he misinterprets her gift of Valentine's meat and a poem as tokens of affection, rather than her making an attempt to blend in and insult him, and cause him great 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 big 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 (Jhonen doesn't approve of them getting together out of all the pairings, as he has confirmed countless times), although it is clear that she hates him. Zim also mentions he plans to destroy Tak after using her to study human affection, which hints that he has never cared for her at all.
An early unpublished animation shows Zim kissing her hand out of respect, and her smiling and giving him a big hug before they walk off together, but Jhonen immediately disapproved it and it was left out of the final version of the 'love montage'.
Had the series 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 (like a dog show or athletic competition). 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.
According to one of the plots for Invader Dib (the series finale), Zim would end up punishing Tak to exile on Saturn along with Dib, The Resisty and the Meekrob; she would have been accused of conspiracy to commit genocide on her own people in exchange for Zim's defeat, which he would immediately accuse her of treason; yet it is unclear if Tak would have sided with Dib and the Resisty.
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.
Facts of Doom
- Outside of the Invader Zim universe, fans like to ship Zim and Tak together as if they were in a relationship. This pairing is known as ZATR, however this is non-canon and Jhonen has said that he doesn't support it.