I have an Link Electronics IEC-788 Closed Caption Decoder.

When I have it connected, the input signal is distorted. Bad captions and visible distortion on the output. When I manually short circuit the ground of the input and the output, the distortion is gone.
How can I fix this issue?

Bad captions implies that the problem is on the input rather than the output. You could open the device's cover and see if the input video jack/panel is loose. Tightening nuts/screws or re-soldering pins (if you can) may fix the problem. Let us know what you find when you remove the cover.

I could not find any damage to the board. I did find that the ground of the input stage is not connected to the ground of the device itself. That’s probably by design, decoupled?

Anyway, I was fiddling around with the device and the short circuit trick of connecting the gnd from the output to the gnd of the input didn’t work anymore.

But I’ve now fixed it the following way:
- ld player connected to receiver by s-video
- s-video output from receiver connected to the cc decoder.
- Cc decoder connected to projector by s-video.
- still distorted, in order to remove the noise, I’ve connected the composite output of the cc decoder to a composite input of the receiver. This removes the noise.

Hmm, I would not expect any "decoupled input" connections on any common home-video equipment such as we are discussing. And, your "extra" composite-out-to-receiver-in connection is in fact completing a ground connection for the CC decoder's input relative to its video input.

The important thing is, your problem is fixed. Very good.

I read this in the specsheet

My thought was that a 'differential input amplifier' amplifies the difference between the gnd and the hot wire of the input signal, and not connecting the input signal's gnd to the chassis. But that goes a bit beyond my knowledge.

I'm happy with my fix, but it somehow still annoys me