hacking a toy rc car I don't understand two little things
The motor in the picture is dc and it will create some commutation noise so the cap helps suppress this and probably means that the RC antenna works better.

The white cable going to the foil is odd so i can't give a definite answer but maybe suggest it is part of the RC antenna scheme. It may not even be a wire - it could be a vent for the batteries.

If you are going to control the motor via PWM you might find that the cap needs to be reduced. It's a 100nF cap and it might be a little too high for the PWM so try 10nF.

Also use two wires to the motor that are twisted with each other to prevent emissions affecting other circuits in the car especially the antenna.