To the powers that be and anybody that sees this problem:
I've found that when I delete a .h file in CW10 and then rebuild, I get an error saying that the .h file is expected in SourceFile.obj (SourceFile being whatever .c the .h was originally loaded into).
To correct the problem, I go into the SourceFile.d file found in BoardType_Int_Flash_Debug|Release - Sources and delete the reference.
In changing/saving the SourceFile.d, I get the message saying that it is a derived file, am I sure I want to do this and I say "Yes".
After doing this, the project builds without any issues.