It‘s the same kind of paradox as Tasha going back to the past with the Ent-C and thereby erasing her own past.
It‘s the concept of a time remnant to borrow from Flash terminology.
There is precedent in Trek for this.
Its actually a lot more complex.
There are three actors (Dr Burnham/Burnham/AI) who are jumping backward and forward in time.
Moving forward in time is the safer option but when you also add that the AI then sent something back in time as well it starts to get really messy but its manageable, similar to a predestination paradox like we saw with Tasha and her daughter Sela.
The action that really makes it a gigantic problem is Burnhams/Pikes intent to undo the AI actions in the future by destroying it in the present, which means any action it took in the future will no longer have happened, which includes the sending back of the probe by the AI to the past which is what sets all of this off in the first place.
Hence the possibility of a reset as has been discussed in the thread, the writers can just ignore it but after the effort they put into it to align it with ToS I find it rather unlikely, I think there is more for us to see in regards to it, especially the actions of Burnham and the Discovery in the future and maybe what remains of Leland/AI that is currently in the spore chamber.
The only ones who will be aware of the change will be those who wear the time suit or have any interaction/proximity with the time crystal which could end up including the Discovery itself and the Enterprise, if the AI is truly defeated they can go and get themselves another time crystal if need be.
I do think that the present is safe from the AI, but the future is still up for grabs which is what we will see in Season 3, we dont have all the facts yet as we havent seen what Burnham and the Discovery will do in the future yet, they could make it worse before they make it better.
There is also the matter of Georgiou who will need to return to the present if she is to be a part of the upcoming S31 show.
This is the problem when you take time travel out of Pandoras box, you cant put it back again and it complicates everything, all of this is based on it being in just the single timeline, if the writers were to start adding the MU and alternative timelines it would very quickly become unworkable.
I have a sneaking suspicion that it could have been the cause of the bust up in the writers room, it really does cause all sorts of problems if it isnt thought out very carefully, you can do pretty much anything using time travel but it also has to make sense at the end.
Some on this forum just want the storyline to be over and done with and I can certainly understand why however I dont think it is quite as over as we are being led to believe but only time will tell.