I have been unable to find any information on that particular type of files (Grundig .gr files).
I suspect that it might “simply” be a more known format which they have given a proprietary file extension. I would suggest that you download the VLC player and then attempt playback of the file after renaming it to different extensions such as .avi, .mkv, .mpg, .mp4 etc.
Another option it to attempt to open it in a multimedia file inspector application (to find out which particular codec/compression scheme was used). You can find such programs in our tools section or from this page (fourcc.org).
Lastly, of course, you might consider contacting Grundig support - they should have an idea of what it is :-)
I have same problem. I have a Grundig TV that store video in a .gr format (Grundig specific). I tried all suggestions and not go any. If somwone knows how convert ".gr” grundig files to somelse please post here. Thanks.