Thermostat 2 wires into G

[JAM7]

I am replacing my Alicestaire thermostat for a Honeywell smart thermostat. On my old one there was a green and white wire that were both connected to the G.  In the new thermostat the wires both won't fit.  Why would there be two wires going to the G? What should be done with the extra wire? 

Thanks!!

[Admin]

We would have to know where the other ends of the wires connect.

It may be for an HRV interlock, but is usually connected differently.