OK, as with all things in life, speak with the experts. I am no expert, but your mitsiyus is totally off. Of the hundreds of people I came into contact with whole I was involved in kiruv, only two or three were not hallachikly Jewish.
I have discussed this issue with the leading outreach groups in the world. Most have received guidance from gedolim that you should be open to anyone who identifies as Jewish, as asking about heritage and lineage will turn people away.
Another organization had a psak that as long as it is less than one in ten, there is no concern with having anyone who identifies as Jewish on your program. If we, the staff, discovered that someone may not be hallachikly Jewish, we were told not to make an issue of it in the moment. Down the line, you can make a mental note and focus on some people, but even they have seven mitzvos, and being a ma’amin is a big deal.
Tachlis, not an issue.