I'd say not use the thermal grease and use the strips. Those strips are more akin to a putty-ish compound. My cpu came the same way and I found it much more convenient than using the thermal paste I had also bought. Adding the grease to the paste already on your heatsink might make even more of a mess, something I don't think you want going on in your motherboard.
And if you're uncomfortable using the gray compound, you can wipe it off and apply the grease later on if you want, also.
Also, the difference between using the thermal grease you bought and the factory applied thermal strips is gonna be negligible. The strips are more than adequate to transfer heat as cpus nowadays are much more efficient. But if you wanna go the extra mile anyway and apply the thermal grease, just remove the strips with rubbing alcohol and some kind of towel or wipe that doesn't leave fuzz and whatnot.