You need to open the database in Access (holding the shift key down) and then go to the DATABASE TOOLS tab and find the LINKED TABLE MANAGER under the DATABASE TOOLS GROUP (on the far right).
Then when that pops up, select all of the ODBC linked tables by using the checkboxes or the SELECT ALL button and then click the little box on the bottom left that says something like "always ask for new location." And then click OK. You should only have boxes selected for ODBC linked tables and that way it will pop up the ODBC DSN selection screen and you can select your modified DSN. And then click OK and it should relink.