diff --git a/core/modules/ckeditor/tests/src/Kernel/CKEditorTest.php b/core/modules/ckeditor/tests/src/Kernel/CKEditorTest.php
index dbd11da7b6..2923c52aec 100644
--- a/core/modules/ckeditor/tests/src/Kernel/CKEditorTest.php
+++ b/core/modules/ckeditor/tests/src/Kernel/CKEditorTest.php
@@ -275,6 +275,7 @@ public function testBuildContentsCssJSSetting() {
     \Drupal::service('theme_installer')->install(['bartik']);
     $this->config('system.theme')->set('default', 'bartik')->save();
     $expected[] = file_url_transform_relative(file_create_url('core/themes/classy/css/components/media-embed-error.css'));
+    $expected[] = file_url_transform_relative(file_create_url('core/themes/classy/css/components/media-embed-edit-button.css'));
     $expected[] = file_url_transform_relative(file_create_url('core/themes/bartik/css/base/elements.css'));
     $expected[] = file_url_transform_relative(file_create_url('core/themes/bartik/css/components/captions.css'));
     $expected[] = file_url_transform_relative(file_create_url('core/themes/bartik/css/components/table.css'));
diff --git a/core/modules/media/css/plugins/drupalmedia/ckeditor.drupalmedia.css b/core/modules/media/css/plugins/drupalmedia/ckeditor.drupalmedia.css
index 8866cf47ea..e5813d943d 100644
--- a/core/modules/media/css/plugins/drupalmedia/ckeditor.drupalmedia.css
+++ b/core/modules/media/css/plugins/drupalmedia/ckeditor.drupalmedia.css
@@ -21,16 +21,6 @@ drupal-media {
   text-align: center;
 }
 
-/**
- * Fix positioning without delete button. Overrides
- * core/modules/media_library/css/media_library.theme.css.
- * Can be removed with this issue:
- * @see https://www.drupal.org/project/drupal/issues/3074859
- */
-drupal-media .media-library-item__edit {
-  right: 10px;
-}
-
 /**
  * Allow alignment to display in CKEditor.
  */
diff --git a/core/modules/media/src/Plugin/CKEditorPlugin/DrupalMedia.php b/core/modules/media/src/Plugin/CKEditorPlugin/DrupalMedia.php
index 852c9b316c..c3aff900d6 100644
--- a/core/modules/media/src/Plugin/CKEditorPlugin/DrupalMedia.php
+++ b/core/modules/media/src/Plugin/CKEditorPlugin/DrupalMedia.php
@@ -124,8 +124,6 @@ public function getCssFiles(Editor $editor) {
     return [
       $this->moduleExtensionList->getPath('media') . '/css/plugins/drupalmedia/ckeditor.drupalmedia.css',
       $this->moduleExtensionList->getPath('system') . '/css/components/hidden.module.css',
-      // Add media_library.theme.css for edit button styling.
-      $this->moduleExtensionList->getPath('media_library') . '/css/media_library.theme.css',
     ];
   }
 
diff --git a/core/themes/classy/classy.info.yml b/core/themes/classy/classy.info.yml
index 5f46a6eaa6..a8d1d707c4 100644
--- a/core/themes/classy/classy.info.yml
+++ b/core/themes/classy/classy.info.yml
@@ -32,3 +32,4 @@ libraries-extend:
 
 ckeditor_stylesheets:
   - css/components/media-embed-error.css
+  - css/components/media-embed-edit-button.css
diff --git a/core/themes/classy/css/components/media-embed-edit-button.css b/core/themes/classy/css/components/media-embed-edit-button.css
new file mode 100644
index 0000000000..e09f00b7e3
--- /dev/null
+++ b/core/themes/classy/css/components/media-embed-edit-button.css
@@ -0,0 +1,38 @@
+/**
+ * @file drupal-media.css
+
+ * Styling for drupal media CKEditor plugin.
+ */
+
+/**
+ * Embedded media edit button styles.
+ *
+ * We have to override the .button styles since buttons make heavy use of
+ * background and border property changes.
+ */
+drupal-media .media-library-item__edit,
+drupal-media .media-library-item__edit:hover,
+drupal-media .media-library-item__edit:focus,
+drupal-media .media-library-item__remove {
+  position: absolute;
+  z-index: 1;
+  top: 10px;
+  overflow: hidden;
+  width: 21px;
+  height: 21px;
+  margin: 5px;
+  padding: 0;
+  transition: 0.2s border-color;
+  color: transparent;
+  border: 2px solid #ccc;
+  border-radius: 20px;
+  background-size: 13px;
+  text-shadow: none;
+  font-size: 0;
+}
+
+drupal-media .media-library-item__edit {
+  right: 10px;
+  background: url("../../../../misc/icons/787878/pencil.svg") #fff center no-repeat;
+  background-size: 13px;
+}