Unfortunately, there are major issues with this approach.
The vendor claims "lab-level accuracy" (conveniently omitting the actual accuracy numbers), but the test is a lateral flow test, which means its Limit of Detection is going to be orders of magnitude worse than molecular tests. Tick tests do not require FDA clearance, so their claims are most likely unreviewed.
Existing lab tests for ticks are almost universally based on PCR.
Ticks are small (especially nymphs) and extracting enough material can be tricky even for molecular testing, so I can't imagine an LFT test working terribly well, especially for nymphs, which are responsible for a lot of Lyme infections due to being easy to miss.
The other, bigger problem is that the test result is mostly useless.
The risk of Lyme transmission from an infected tick ranges rougly from And you can't trust negative results either due to limited sensitivity, so you can't rule out transmission either.
In my opinion, tests like this can lead to worse overall health outcomes due to unnecessary treatment or withholding prophylaxis from someone who otherwise qualifies.