Restoring Q Mac 2007 files

I'm not sure what question you're asking… Do you have Quicken 2007 data files you want to use on your Mac running Monterey? Or is this a question about restoring from a backup?

As you likely know, Quicken 2007 is a very old application. Its a 32-bit application and cannot run on any version of macOS which only runs 64-bit applications. So macOS Mojave is the last which can run Quicken 2007; macOS Catalina, Big Sur, Monterey, and next month's Ventura cannot.

But the current version of Quicken Mac can convert Quicken 2007 data files into the modern database. You'll just need to purchase a Quicken subscription and direct the program to start with a Quicken 2007 data file so it can perform the conversion. There's a bit of a learning curve, but I think the vast majority of Quicken Mac users are satisfied with the new program once they get used to it. 

If you're asking for specific help with any part of this, please post again and provide more details.