score:2

generally, you would have to add another tablecell to your tablerow inside tablehead since the body is not linked to your header row.

i would recommend naming the header of this column something like "actions" in case you add more "actions".

<tablecontainer component={paper}>
      <table>
        <tablehead>
          <tablerow>
            ...
            <tablecell> actions </tablecell>
          </tablerow>
        </tablehead>
        <tablebody>
          ...
        </tablebody>
      </table>
</tablecontainer>

if you want to add a tooltip, you can try wrapping it inside a tooltip component (material-ui tooltip)

<tablecontainer component={paper}>
      <table>
        <tablehead>
          <tablerow>
            ...
          </tablerow>
        </tablehead>
        <tablebody>
          ...
          <tooltip title="save user">
             <button/>
          </tooltip>
        </tablebody>
      </table>
</tablecontainer>

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