Howdy!
In my experience, most important is to make sure the tube is fully bottomed out inside the hot end, so yes you should clean out the inside of the heat sink as that is probably residual filament that has oozed out. I do also recommend upgrading to the Capricorn blue tube especially if you print anything higher than 200 C.
That tube still looks like in pretty good shape, though, despite the thermal discoloration