Regarding whether the feat is valid or not - it's ambiguous whether Buzz tried to erase Woody there and failed, or if Buzz didn't even try to erase Woody in the first place. That ambiguity leads me to lean on saying it shouldn't be listed as a feat. The onus is on the writer of the profile justifications to prove that a feat happened the way they claim it happened, not on the people discussing it to prove it did not happen the way they claim. In cases like these, where there are multiple interpretations of the same scene and we are trying to draw inferences, I'd only opt to pass this if there was very clear reason to believe that's how you were supposed to interpret it. When dealing with children's show logic, I don't consider "Buzz wanted to kill Woody" to be compelling enough to warrant that inference.
Children's program?
It is common in Woody Woodpecker to use weapons, alcoholic drinks and constant deaths. Seriously, there's even a joke about shooting yourself in the head in this series.
Woody himself is known for making his antagonists hell on earth simply for fun, as in the case of the police officer who was just doing his job and Woody drove him crazy to the point where he was hospitalized just because he was fun.
Buzz himself tries to kill Woody throughout the series, and he has also been killed a few times by Woody.
Literally in this episode of the plot hax, Buzz at the beginning was blown up by a cannon to the point of turning to ashes (and then regenerating)
And throughout the episode he used the pen to stop Woody whether with sharks, bombs or explosions.
So yes, I think this scene should be interpreted like this.
Buzz tried to kill Woody explicitly on screen throughout the episode. He had the power to erase things and he could have done that. In this case, he did, literally the first thing he did was delete everything, which included characters that were deeper in the background.
I think it's kind of ridiculous to think that Buzz in character, a guy who has already tried to kill Woody countless times, wasn't aiming for him when he erased things or that he didn't even consider using this ability on Woody in the episode where Buzz was trying to kill him for the fiftieth time.