Are hardware store themocouples food safe?
You are correct to be concerned.

In all likelihood, the hardware store thermocouple is not suitable for food use as it would contain metals you don't want to ingest. Here is a table of industrial grade thermocouple materials, note presence of some undesirable metals:



Source.

You would want a thermocouple specifically made for food use. Example. I found that one by searching NSF thermocouple, a cautious approach since NSF (National Sanitation Foundation) certification entails high standards. But most thermocouple advertised for food should suffice, such as this $16 one.