Text Burner works over the internet and therefore it is not linked to your real number in any way. When you open the Text Burner app, it acts as a software that connects to the internet for text services, and therefore it does not use your telco-registered number and there no way to use a
Phoner number to trace this back to your real number.
The only time your identity might be known is if you reveal or hint your identity information through text by accident.
Will people know my identity?
