Jo I didn't understand that was what she was doing. Reguardless though, some countries ask for a police background check from all counties you've lived in the past 5 years. It's not that Thailand has jurisdiction in Eupope, just Europe wants to see if she's committed crimes here.
Luc I tagged Tob because I was hoping he could show you the post. Idk where it is. As for filing a TM30, you only need to do it once for as long as you live at that address. You can come and go as many times as you want, as long as you live there you can use the receipt for 10 years.
Where are you now? If you're applying for a teaching position or certain visas inside Thailand, you need a Thai background check (as well as one from your home country). If you're applying from outside of Thailand you only need one from your home country.