No.

Who hurt you?

The best part is the leading image of the Pillars of Creation is from the Hubble.

Here is a comparison of the HST and JWST side by side: https://webbtelescope.org/contents/media/images/2022/052/01GF44EV0PPW2BHJS9HMA1AGEK

Backdoor implies it was deliberately put there. Looking at the CVE it does not seem intentional so just an exploit.

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There is sufficient drag in Low Earth Orbit for the crafts to deorbit without station keeping, meaning they burn up in the atmosphere within a few months/years depending on atmospheric conditions.