Can separated teak pieces on table be repaired?  

Looks like the gap extends deeply enough into the joint so it will still be there even if you sand the halves into plane (flat).

For repairing split glue joints in solid tabletops like this, best practice for permanent results is to disassemble the table, split the top along the failed seam, joint mating surfaces, re-glue the top, reassemble the table, and refinish.

Thank you. Taking it apart and re-joining is definitely beyond my skill level. So are you saying you think sanding it flat would only be a temporary fix, and it would keep expanding and do that again? Or are you saying it would still show even if sanded?

Looks to me that the split will still be visible after sanding flat. The glue joint has failed due to either movement caused by water/moisture exposure or internal stress in the wood, or, more likely, both. You could sand it flat and fill any remaining gap with wood filler of some sort, but that approach rarely lasts, IME.

OK, thank you. I guess it isn't in the cards then!