Step 1: Open it up
Once the screws are removed, pry apart the back panel of the motor. You may be tempted to split it in the middle, as this will seem like the natural place to open it up. However, if you split it into two parts as such, it will spill out all the gears and be a mild pain in the neck to put back together.
Step 2: Desolder
Remove the solder from these with desoldering braid.
Step 3: Pry it apart
It is a good idea to save this circuit board, as it can function later as a small low-power H-bridge circuit for connecting a small motor to a micro controller.
Step 4: Connect new wires
If there is a marking to indicated one lug is power and one is ground, connect the red one to power (or red to red, as in this case).