It seems that Reagan was involved from very early, but Book It! was created by Pizza Hut folks:
> Book It! was conceived in 1984 during a dinner with Art Gunther, President of Pizza Hut, and Bud Gates, SVP of Marketing at Pizza Hut, as a way to help Gunther's son read more.
This is not at all to discount how Reagan championed Book It! specifically. He also worked on other literacy projects, and declared 1987 the Year of the Reader.
> Like many simple plans, this one was hard to realize. Beginning last January, Gunther met several times with Secretary of Education William Bennett, representatives of President Reagan’s Task Force on Private Sector Initiative, and teachers’ and school administrators’ groups. With input from the educators, Gunther and his associate Sharon Knight designed a program.
Considering how involved he was in the project and how early, I'm won't quibble on this point, since you said sort of invented. I don't see how it would have had the success it did without his involvement and efforts, but he didn't invent it strictly speaking.
