You need to tell Visual Studio that you deleted the files.
Go to the project/solution folder where the files existed and remove them there.
Visual Studio assumes that since you added the file originally, it should be published. It can’t assume that you don’t want it just because it isn’t in the filesystem. Think about using source control in a team – the file may only exist in one persons’s machine, but still be needed.
This is not a difficult as you think – the files that can not be found have a semi-transparent look to them, easy enough to select these and bulk delete in Visual Studio. You can also set the project properties to display all files then select all the ones that need to be part of the project and add them in a single operation.