This script is an enhanced version of Chris Gamble's Google Meet Grid View script. It addition to providing all of the grid view functionality, it also registers whether or not expected attendees joined the Meet.

It adds a text field to the Join page where you can type or paste a list of the expected attendees. As participants join the Meet, the list gets updated - a check mark is prepended to the names of expected attendees; unexpected attendees are appended to the bottom of the list.
I believe that this makes it a lot easier to know whether or not students actually joined (although, it does not record when they joined, when they left or if they actually paid attention).

In Chrome:

1. if installed, turn off the Google Meet Grid View extension (chrome://extensions/)

2. add the TamperMonkey extension (https://chrome.google.com/webstore/detail/tampermonkey/dhdgffkkebhmkfjojejmpbldmpobfkfo?hl=en)

3. restart Chrome

4. install my version of the script: https://openuserjs.org/scripts/Al_Caughey/Google_Meet_Grid_View_Attendance

5. launch a Google Meet (https://meet.google.com) and start a meeting

6. paste your class list into the field on the right side of the screen. The format of the names may be somewhat system dependent... in my case, my students appear with first name followed by last name (without an email address). You might have to alter the format of your initial list.
   When you leave the non-empty field (i.e, click outside of the field), it will hide in the lower right corner of the screen; if the field is empty, it will not hide.
   If you hover over the 'hidden` field or click within it, it will pop-up to full size again

   As participants join the meeting, a check mark will be added beside their name if it is already in the list; otherwise they'll be appended to the bottom of the list with a preceding ?

   Click the [-] button at the top of the field to clear all checks from the list of names
   Click the [x] button to empty the field

Privacy
This script does not track any user data. It does not connect to any external server. Tampermonkey may periodically to check for updates but does not transmit any user data.