University lecturer here...
I have to review hundreds of pieces of written work, and have used many AI checkers. Here is the short version:
Most checkers are very good at distinguishing between 100% AI work, and 100% Human work. Their accuracy is very good when it comes to 100% human work, and they are very very unlikely to rate it as 100% AI generated.
However, they are very unreliable when it comes to a combination of AI and human writing. For example:
Human written - AI checked/fixed
Human written - AI improved word choice
AI written - human adapted
Human written - AI translated
etc.
In those scenarios they can be very unreliable and different checkers can produce different results.
AI writing isn't distinguished by being well written or structured though. It tends to be a shallow word-salad that throws in a glossary of key words, in very bland and average sentences. The checkers have a whole load of markers that they use, uniform sentence length, overuse of certain words and punctuation and structures etc. Even without a checker, it is increasingly obvious to anyone who has read quite a bit of AI writing, what is human and what isn't. AI has a style, that you have to work very hard to get AI to remove by itself.
So your own CV is unlikely to be flagged for AI if you did it yourself. The only people who should worry about AI checking, is those who did use AI.
(That being said, if writing is not a competency of the job, then I don't personally see the problem in using an AI app to help speed up a very tedious process)