The WP User Integration add-on has a shortcode for adding a My Events page. That shortcode is:
[ESPRESSO_MY_EVENTS]
There are various icons that are shown under the actions column. From left to right, they are:
Edit registration
Resend registration details email
View registration checkout
View order confirmation
View invoice
These can be hidden by using some CSS. See the examples below:
Hide edit registration icon
/* Hide edit registration icon in My Events page */
.espresso-my-events .ee-icon-user-edit { display: none; }
Hide Resend registration details email icon
/* Hide resend registration details email icon in My Events page */
.espresso-my-events span.dashicons.dashicons-email-alt { display: none; }
Hide View registration checkout icon
/* Hide view registration checkout icon in My Events page */
.espresso-my-events span.dashicons.dashicons-cart { display: none; }
Hide View order confirmation icon
/* Hide view order confirmation in My Events page */
.espresso-my-events span.dashicons.dashicons-media-default { display: none; }
Hide View invoice icon
/* Hide view invoice icon in My Events page */
.espresso-my-events span.dashicons.dashicons-media-spreadsheet { display: none; }
You can add new the styling to your child theme's stylesheet or through a plugin like Reaktiv CSS builder or My Custom CSS.
References: