Instead of Monday, Tuesday, etc., you can have the Month View show the days of the week as the appropriate abbreviations (e.g. Mon., Tues., etc.).
Perform a template override by making a copy of ‘/wp-content/plugins/the-events-calendar/src/views/month/loop-grid.php’ and place it in the ‘tribe-events/month’ folder in your theme.
Look for the following line:
<th id="tribe-events-<?php echo esc_attr( strtolower( $day ) ); ?>" title="<?php echo esc_attr( $day ); ?>" data-day-abbr="<?php echo esc_attr( $wp_locale->get_weekday_abbrev( $day ) ); ?>"><?php echo $day ?></th>
Then replace that with this new code:
<?php $short_day = esc_attr( $wp_locale->get_weekday_abbrev( $day ) ); ?>
<th id="tribe-events-<?php echo esc_attr( strtolower( $day ) ) ?>" title="<?php echo $short_day ?>" data-day-abbr="<?php echo $short_day ?>"><?php echo $day ?></th>
The idea is to grab the short form of the weekday via WordPress’s locale helpers, then use that in the table header (including the title attribute – though it may be preferred to use the full-length text here).