If you reproduce copyrighted material in a way that requires permission from the author, it is best to include a statement that it is reproduced with permission, so that people do not think you have infringed someone's copyright.
But if you convey the same information as an existing source, with your own words and (if applicable) your own images, then you are not at risk of infringing the original author's copyright. In this case, it is still important that you cite the source, for reasons of integrity and good scholarship. But since you have not included any material from the copyrighted source, permission of the original author is not needed. Since permission is not needed, there is no need to include a statement saying that you have obtained permission to reproduce the original work, even if you have obtained it.
To put this another way: If you have permission to reproduce a work (or parts of it) as-is, but you instead make your own work that uses information from the original work but does not contain any part of it, then you have not done the same thing that you've asked permission to do. What you have done is still OK (though you should cite the work as a source). But it is not what you needed to ask for permission to do, it's not what you got permission for, so there is no reason to include information about the permission you received in the work.
If you get permission from the author of a copyrighted work to reproduce the work (or some part of it), and then you decide not to reproduce it, that's fine. That seems to be the case in this instance.