You have some reference somewhere on a layout, script or calculation that refers to this file by name. When you open it on your local system, chances are that it finds this file and opens it. (Check Windows | | Show Window and see if it's listed there). On the server, it can't find the file and you get this error message.
Open Manage | External Data Sources and look. I predict you'll find an entry there that refers to People Database Copy.fp7 that needs to be removed or changed to make this dialog stop appearing. It would be wise to check carefully to see what elements of your system refer to this before you remove it to see if you can safely do so or if you need to redirect this reference to a different file used in your system.
FileMaker's Database Design Report can be very useful for this as you can generate the DDR, open it in your web browser and do a text search for the data source name to discover where it may be in use.
*facepalm* duh. of course. i should have caught that. i did have it linked to the backup copy while the network was down. thank you!