Get as much (paste) as possible off. I will use a toothpick, chop stick or other firm but pliable means to remove all of it. It can and should be done if one wishes to be proper and safe about maintaining your (or others) machine(s). 'Prolly shouldn't, but I use Windex and a soft paper-towel to remove residue from chip table... always spotless when done.
Honestly: No. That mess should be cleaned properly and acceptable replacement thermal conductive material should be acquired. The only reason I am being hard is that if proper heat dissipation is not provided and adequate; one will have a useless/broken laptop. This I do not want as it would seem that you are here looking for dependable and/or knowledgeable advice, no?
Let's get it right the first time so one does not have to open the casing for a few years to come.
Edit: Please post a picture of the underside of metal piece that connects to chip-set. The heat sink itself. I want to see what surface that sits atop the chips.
Edit: Service Manual .PDF (in case one hasn't the paperwork already).
The only thing I do not agree with (from what I read) is the following:
"The original thermal grease can be reused if the original processor and heat sink are reinstalled together."
^^^ This may be true but seems fool-hardy and maybe some misinformation in order to burn chips and sell more? Nah... what am I thinking?
Yes: The chip circled in red does indeed require some thermal conductive material... be it paste, pads or copper shim. It appears that the heatsink covers all of the chips and more. Especially with the dedicated graphics in the laptop... be very careful as there are literally thousands of post on the interwebs of issues with burn GPUs. This does not have to be the case here.
Edited by bludgard, 15 May 2017 - 09:20 PM.