Increasing range on a 315Mhz transmitter

Adding a length of wire may detune the output stage if it's been optimised to suit the pcb track design and reduce the signal strength

The receiver has coil of wire attached to it. Would it be best to straighten this out, or leave as a coil?

The transmitter-fob has no such wire. There is no obvious sign of any antenna etched into the pcb, assuming there isn't one (yet) then, with reference to the circuit diagram on the datasheet I linked to, where should the wire go?
thanks