I've just had a thorough look through Butler and it doesn't look like there's a way to automatically add a note/activity if someone has opened the card or board.
However, if you bring up the board settings by clicking on 'Show Menu' in the top right, there is a board activity section that might give some details, although it only seems to be for things like 'Esme moved X list into another board' and things like that. It doesn't seem to give details when users were active.
If you click on the individual members' avatar at the top there's an option to see member's activity. I only have my husband on mine, so I can't see very much activity, but if you have lots of members, you might have more luck there?
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