If you did not let the wires get moved around a lot, and you don't suspect that they may have a bad connection at the driver, then you don't need to take the driver out. Just expose the solder at the pins, and load your tip with a little solder. Then touch it to the pin while slightly pulling on the wire, and it will unsolder almost instantly...
If you have to take the driver out, you just have to carefully pry it up from the edges. The tape is very sticky, but if done carefully, you will be able to pry it up.
If you do this, then you will be checking all solder connections. If you can use the first method, and unsolder the wire from the diode, you would still be able to put a bit more solder on the top side of the FlexDrive to make sure of the connections without necessarily removing the driver.
But as you can see, the driver is very small, and you need a fine tipped solder iron. Make sure your tip is clean, pre-tinned, and a little flux on the solder is also very helpful...