In situations like that you want the wood very dry, slender knife to run down in the gap and clean out as much as possible before trickling in epoxy. Epoxy can be worked in by using a spatula or putty knife and putting on epoxy, sort of poking it down the slightly widened gap with the blade of the putty knife repeatedly until you feel good about it.....more is better than less. Then clamp the surfaces with a pre set clamp...so as to not waste any clamp time...and let'er set. I often add a mite of WEST carbon into the epoxy to make it black as it will be a bit exposed to the UV after it cures.

BUT...FIRST....you have to acetone it out WELL. Like painting, prep is 90% of the job. A clean gap is a happy gap. Do the acetone much like you will do the epoxy. Sort of scoop it through the gap with the sharp edge of the putty knife several times. Scoop in acetone, scoop out whatever might be "in there", it could be debris from prep or oils from the teak. The teak oil WILL interfere with gluing which is why you're in the fix to begin with...most likely.