Originally Posted by GMFL
What would make you think the varnish would crack?......
.....You could make an argument that the varnish won't adhere to the caulk...
You are right, fresh real varnish (is that what you're using?) is flexible and will endure the different adhesion and expansion rates for a bit.
However, it just has to give up the ghost on the caulk before the wood.
Not that you're inclined, but I agree not to dig out the caulking after you varnish. It would leave an edge to the varnish on each side of the caulk that would allow water beneath. I also suspect the varnish wouldn't cut away neatly either.
Back to removal of the remnants from the caulk, have you considered a 2 part acid teak cleaner? I'm not sure if it will remove the varnish bits, but you many want a good cleaning of the teak before you reseal anyway. Maybe worth a shot.