Hello: I’ll guess that device in the thermocouple is a high limit switch; probably a one time use type. That is, it can only get overheated once and then you need to replace it. It’s part of the safety system in the heater. From your original post, it doesn’t seem things overheated or you could not relight it. So, you may not need to replace it at all, but rather make sure there is a good flame on the thermocouple. A dirty pilot orifice, or low gas pressure could be the problem. Thermocouples should be heated up so the tip of the unit glows a dark red. Is yours doing that? If not, it might not be consistently generating enough power to work the gas valve. Does that make sense?