how can I update specific columns (those modified in excel file) back to access table after?
Either Access is the "master" or Excel is the "master". Having two sources for updates to data is the road to unreliable data.
If you want to import updates from Excel, you CANNOT do this by linking to Excel and joining to the Access table and running an update query.
WHY? Because linked Excel tables are not updateable and that renders the join to the Access table not updateable.
Therefore, you need to import the Excel file into a temp table and then run an update query using the temp table rather than the linked table.
Importing data like this makes Access bloat so you might want to use a tempBE and import into that so you don't bloat your FE or BE. We can advise if you want to do that.