If it reproduces by cloning, it should be relatively easy to eradicate at once. You only need one specimen...
- But aren’t the ants even worse?
- Yes, but we’re prepared for that. We’ve lined up a fabulous type of spider that thrives on ant meat.
- But then we’re stuck with spiders!
- No, that’s the beautiful part. When wintertime rolls around, the spiders simply freeze to death.
So the climate change does solve the problem. Just have to take it far enough to combat these species.
So, no, you don't just need one specimen.
Modulo any environmental or self-mutation factors, I suppose? Might be that a tick which sucks blood from deer with XYZ picks up a parasite or bacteria which protects it against your measure. Or one crawls through some chemical goop / radioactive slop / gets hit by a cosmic ray etc. and gets a mutation which helps.
(Both fairly unlikely, I'll grant, but when you're dealing with millions or billions of ticks, unlikely is likely to happen a lot.)
But anyway another comment says these ticks also can repro sexually so whatever
But of a manufactored virus or bacteria I have not heard yet. And I think it would be way more dangerous.