Is it permissible to use a digital version of the "Colored Tajweed Mushaf" in an electronic program, given that there are copyrights prohibiting its copying and distribution?

The Tajweed Mushaf is a human effort not devoid of observations and errors. The discussion is not about the words of Allah, but about its innovative presentation method, which is an intellectual right of its owners and must be preserved.

It is permissible to use a printed copy of the Mushaf without the permission of its owners if there are no other beneficial uses for them from what you are asking about. So, if the publishing house does not have a mobile application for the Mushaf, it is permissible to create a free application for its benefit, due to the difference in uses.