One of my bids for geothermal includes electric back-up strips. The contractor said one needs them in case the geothermal "goes out." The other contractor never mentioned anything about it and has not included that in his bid. Can anyone comment as to the need for these electric back-up strips?

Most geo systems offer less heating BTU's than the indicated requirement. In my area, therefore, we need a supplemental heater. This could be an existing furnace in concert with a split system or an electric coil on a package unit etc.... The electric coil generally costs less as it can be used at the same time while fossil units shut the geo system down.
While you could certainly have enough geo loops to avoid auxillary heat, an electric coil may do for $100/yr what might take 2 tons of loops + additional ductwork and higher appliance cost (maybe 6K).
Your other contractor may plan on an auxillary heater as well, but not have mentioned it.
Hope this helps.
Joe

for resistance heaters and any other sup. heat coupled with geothermal outdoor temp sensors must be used set to turn on the sup. heat at the balance point of the system on a single zone system they can be wired directly to a honeywell pro 8000  but with a zoned system a duel fuel control should be used. if its just incase of a faluire its not a bad idea there cheap and offer some security that you wont go cold ( unless your blower moter goes) but should be wired to a disconnect switch by the unit access not only to the t-stat so they wont be turned on by accendent because they are much less eff then what you are paying for