But instead it looks like teak sections are solid areas of teak wood with grooves just for decoration. Is it the case?
I don't think so, if you look at the grain it shows these are individual planks with a rebate cut on one edge to form the groove.
Not sure I got it... It looks like old caulking is siting in the bottom edges of the groove. I even started to deeper the grove with my fein tool since it was only 3mm depth, and it was hard to remove old caulk from bottom edge. If this is rebate cut, then is it save to deeper the grove?
Ok, now I got it. I guess you mean rebate looks like on attached picture. In this case there is nothing wrong with making groove more deep, because this basically remove (or cuts) the rebate, which actually increase effective teak thickness ( anyway, rebate is not required any more)
Correct?