@Denis,, Another reason could be, the exhaust pipes are rather high above the area where they come out of the funnel and this construction could help to decrease vibrations all the way up to the top of the exhaust pipes, kind of stabilize them.
also possible like buying a car,,you can get different models, same with ships,,some owners let it fit others not. But knowing that during starting/maneuvering the engines in general sooting the most, but the speeds do not create the wind to blow it off
i would think to prevent too much soot falling down on the decks below could be also a good reason.

And it keeps the ensigns dry.

Hmmmm, I think seen that way I can live with it :-))

Well both of them have similar looking afts... VERY similar, that once I see such Peters feeder I automatically think it's a Sietas one until I look closer.

SIMILAR looking Sietas feeders??? Denis, that's devastating, comparing apples and oranges! 😁

To make Hugo Peters' feeders be a little more distinctive from similar looking Sietas feeders? :D

These deflectors are to give personality and exclusivity to the boat, so that its constructor presumes of design, otherwise in a ship with the funnel so aft is not necessary to fit deflectors.

I thought normally deflectors used when there are air intakes at the back of the funnel.
Ted, if what you said is correct then why they aren't that common?

Built by Hugo Peters Shipyard Wewelsfleth,Germany.

I think it's a 'smoke deflector', which princip is the same as it was used at a steam-locomotive.

To catch soot when starting and blowing the engine

Pretty big screen on top of her funnel... I wonder what for?