Teak decking, seats, etc. is meant to go grey. You clean it preferably with saltwater (fresh will do in a pinch) and a brush, scrubbing perpendicular to the grain, never along the grain. Ideally you do this as rarely and as gently as possible, because each time you scrub it, you're irrevocably removing some of it. You can then spray it with a biocide (Patio Magic, Lidl's Baufix or similar) to keep green growth off it for a while, which extends the time between scrubs. Some people oil theirs or "restore" it with expensive 2-part acid products, but those people also eat children.
Caulking standing out of the teak can be cut or sanded down, but that's hardly worth it as the teak decking on Bavarias is fairly thin and by the time your caulking sticks out significantly, you'll soon meet the plywood base it's glued on (you can check how much remains in some areas by removing a deck fitting to expose the edge). When that happens, it's time to renew it, which is a rather lengthy and expensive job. Or get rid of it, although you'll then have a most awful time trying to clean the glue off the gelcoat underneath. Or put on PVC fake teak (Dek-King, Plasteak, etc.), which looks dreadful and wrong but lasts forever.
Exterior teak trim (anything you don't sit/walk on) can be treated in exactly the same way and left grey, although it will last much longer if varnished. That means either taking the bits off, or masking them off to do it in place.
Varnish over epoxy will last even longer, but can be tricky to apply and has various ways of going completely wrong. You can also use a modern hybrid coating like International Woodskin (formerly/elsewhere known as Cetol), which is easier than varnishing and protects the wood, but doesn't look quite as nice. You can also oil your teak trim, but real teak oil is very dear, which is why most "teak oil" products are made of mostly linseed oil and kinda suck. Oil will need redoing regularly, a good varnish job will last a few years and longer with more coats or an epoxy undercoat. In each case you'll want to sand, dry and clean the teak before protecting it.
