You will want a product designed for the job, and you should steer well clear of PU based products (Sika) as they don't last too well in the sun. TDS-SIS 440 is the proven goop for the job. Slightly cheaper alternatives are also available, depending on where you are, for example here in Italy you can get Fratelli Zucchini MS Deck Caulking.
I used a thin, sharp knife to detach the old caulking from the sides of the groove and then a sharpened screwdriver of the right width to chisel out the bottom.
Our teak deck is going to come off in a year or two though, as it has annoyed me enough and will be replaced with something more practical that is gentler on the knees