diff -u b/core/modules/media_library/config/install/views.view.media_library.yml b/core/modules/media_library/config/install/views.view.media_library.yml
--- b/core/modules/media_library/config/install/views.view.media_library.yml
+++ b/core/modules/media_library/config/install/views.view.media_library.yml
@@ -567,7 +567,7 @@
           hide_empty: false
           empty_zero: false
           hide_alter_empty: true
-          text: ' '
+          text: ' edit'
           output_url_as_text: false
           absolute: false
           entity_type: media
@@ -620,7 +620,7 @@
           hide_empty: false
           empty_zero: false
           hide_alter_empty: true
-          text: ' '
+          text: ' delete'
           output_url_as_text: false
           absolute: false
           entity_type: media
diff -u b/core/modules/media_library/css/media_library.module.css b/core/modules/media_library/css/media_library.module.css
--- b/core/modules/media_library/css/media_library.module.css
+++ b/core/modules/media_library/css/media_library.module.css
@@ -51,8 +51,8 @@
 .media-library-item .js-click-to-select-checkbox {
   position: absolute;
   z-index: 1;
-  left: 5px;
-  right: 5px; /* LTR */
+  top: 5px;
+  left: 5px; /* LTR */
   display: block;
 }
 
diff -u b/core/modules/media_library/tests/src/FunctionalJavascript/MediaLibraryTest.php b/core/modules/media_library/tests/src/FunctionalJavascript/MediaLibraryTest.php
--- b/core/modules/media_library/tests/src/FunctionalJavascript/MediaLibraryTest.php
+++ b/core/modules/media_library/tests/src/FunctionalJavascript/MediaLibraryTest.php
@@ -107,9 +107,9 @@
     // Check that name is not a link.
     $assert_session->elementNotExists('css', '.media-library-item__name a');
 
-    // Check that there is an edit link.
+    // Check that there is edit and delete links.
     $assert_session->elementExists('css', '.media-library-item .views-field-edit-media');
-
+    $assert_session->elementExists('css', '.media-library-item .views-field-delete-media');
     // Test that users can filter by type.
     $page->selectFieldOption('Media type', 'Type One');
     $page->pressButton('Apply filters');
@@ -442,8 +442,9 @@
     // Assert that no links are within image thumbnails in grid view.
     $assert_session->elementExists('css', '.media-library-open-button[name^="field_unlimited_media"]')->click();
     $assert_session->assertWaitOnAjaxRequest();
-    $assert_session->elementTextContains('css', '.views-display-link-widget.is-active', 'Grid');
-    $assert_session->elementNotExists('css', '.media-library-item--grid .media-library-item__name a');
+    $assert_session->elementNotExists('css', '.media-library-item__name a');
+    $assert_session->elementNotExists('css', '.views-field-edit-media');
+    $assert_session->elementNotExists('css', '.views-field-delete-media');
     $page->find('css', '.ui-dialog-titlebar-close')->click();
     $assert_session->assertWaitOnAjaxRequest();