How can I connect a smart switch lead wire to a screw eye loop from the old switch?
This loop method was a "trick" that was used in the past (and by some old-timers today, probably), but it's not something that an electrician would do now.  The solution is to cut that bare loop so its two wires and then bundle those two with the third wire from the new switch.  Because the wire is twisted, it's best to just cut off the looped section of wire and re-strip a fresh, clean section of wire before bundling them together.  Trying to straighten the loop could cause the wire to break off when tightening the wire nut on the bundle.

Oh, and be sure the power is off at the fuse/breaker before doing this, of course.