I apologize if this isn't the right side, but I've tried to do some digging, but I can't find anything the aligns with her recall of the details.
The story goes that my great great grandmother had been tattooed with a cross to identify her as Christian, and that she destroyed most evidence of my great grandmother's birth because she was afraid she were going to be taken away for not being Muslim. My grandmother describes it as the reverse of the Crusades.
Thank you!
Do you know what time period she was speaking about or where in Syria she was? If she was still in Syria during World War I it strikes me as being in the main plausible. There were other periods in that era that also had pogroms, but nothing as lasting, intense, and brutal as the war.
The story goes that my great great grandmother had been tattooed with a cross to identify her as Christian.
Some Christian communities in the Middle East have a tradition of tattooing themselves in this fashion, for example the Copts in Egypt will often tattoo a small cross on their hands.
The way you wrote it reads to me as though she was forced to carry such a mark, almost by analogy to the tattoos received by Jews in concentration camps during the holocaust. I'm not aware of any such systematic effort at tattooing on the part of the Ottoman government upon Christians in this period.
Syria
It's also perhaps worth noting that "Syria" before the end of World War I referred to Ottoman "Greater Syria", which today includes the modern states and territories of Syria, Lebanon, Israel/Palestine, and Jordan. It's possible that your Great Grandmother might have identified herself as "Syrian" even if she was by the standard of 2018, for example, Lebanese.