https://www.youtube.com/watch?v=FPEiEG4Kzik
I would recommend using a good thermal compound such as Artic Silver 5 and would just remove the Thermal Pad and discard. It's up to you.
Instructions:
How to apply thermal compound
http://www.arcticsilver.com/as5.htm
Thermal Pads tend to be difficult to unstick.
Note! Twist in a clock and anti-clockwise rotational direction, which creates a shear force in the thermal interface. Failure to break the adhesion seal between the HSF and the processor may result in pulling the processor out of the socket, possibly resulting in processor and / or socket damage.
How to uninstall and install an AMD processor and a heatsink / fan in a system
https://support.amd.com/en-us/kb-articles/pages/howtoreplaceamdcpunhsf.aspx
Note! If installing a new retail-boxed AMD processor, the HSF supplied with the processor will already have thermal interface material pre-applied on the bottom surface of the HSF. Do not apply any additional thermal interface material
4. If using a previously installed HSF or a new HSF that does not have pre-applied thermal interface material, apply a 10mm diameter droplet of thermal material located in the center onto the top surface of the processor