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A few ideas:
1) Use SQL create an alias (CREATE ALIAS) to the file in a different library that doesn't have an embedded dot in the lib name.
2) What naming convention are you using in your DSN? *SYS or *SQL? *SYS requires that you use a slash: G.USERLIB/TABLENAME. That might resolve the problem for you. *SQL requires a dot, and is going to be confused by the "G." If you are allowing Access to compose the fully-qualified table name for you, it will probably only handle *SQL - so you'll probably need to use the alias technique. If you are writing VBA code, you can use *SYS, which is more likely to let you get away with the dot in the lib name.
3) Try *SQL naming convention setting the Default SQL Schema or Library on the ODBC Setup Server tab to G.USERLIB, and then use an unqualified reference to the table in your Access code. Just TABLENAME by itself. With *SQL naming, the system will automatically search the default schema.lib whenever given an unqualified table name. *SQL doesn't use the library list.
4) Try *SYS naming convention setting the first library in the Library List (ODBC Setup - Server tab) to G.USERLIB, then use an unqualified reference to the table in your Access code. *SYS doesn't use the Default SQL Schema/Lib.
If you can't get it worked out, post back and explain exactly how you are accessing the table so I can recreate the problem on my system.