With this "modification" done, the Nuvi is permanently enabled. Thus you can use with Nuvi with antenna flap retracted or extended. If you want it back to its original state, just remove the metal foil. Simple

For your knowledge, there is no internal antenna in your Nuvi 650. The flap antenna is the one and only antenna
Re-rad antenna only works to transfer the signal from the external antenna to the one inside the car. The internal antenna signal radiation is sufficiently strong to work within the confines of the car.
If you need a stronger signal for a larger area then the signal needs to be amplified. Simple logic.