A low rent approach would be to open a command window (Start -> Run => cmd) and navigate to the folder with all the SSIS packages.
The find command looks for a specific string (case sensitive by default).
C:\my\ssis\folder > find "myCaseSensitiveTableName" *.dtsx
C:\my\ssis\folder > find /i "myCaseInsensitiveTableName" *.dtsx
That should be a good starting point for looking through your packages and hopefully the table name(s) you're looking for do not collide with the internal xml of an SSIS package. If that's the case, and you can assume OLE DB Destinations, a find for
OpenRowset should be beneficial.