First of all, application having such stupid requirements is not good application.
Second, VFP ODBC driver is 32 bit software and it cannot cooperate with 64 bit software.
But it is still possible to use 32 bit ODBC drivers under 64 OS to work with other 32 bit software. It is just installed in a separate folder - c:\windows\syswow64\ and the ODBC administrator is odbcad32.exe
So, did you use this 32 bit administrator? Probably yes.
DSN definition is just a Registry entry and you have to look for DSN name "dBASE Files" in registry. If you see "dBASE Files" DSN in ODBC administrator then you have to find it in registry. It should occur several times. If you delete all these "dBASE Files" occurences from registry then it should disappear from DSN list.
The dBase driver itself is MS Access driver in fact and it should remain installed after DSN deletion. If you decide to reinstall it then you may find it packed together with MS Office.