Index: src/wp-content/themes/twentysixteen/css/blocks.css
===================================================================
--- src/wp-content/themes/twentysixteen/css/blocks.css	(revision 58196)
+++ src/wp-content/themes/twentysixteen/css/blocks.css	(working copy)
@@ -163,6 +163,10 @@
 	font-size: inherit;
 }
 
+.wp-block-code.has-background code {
+	background-color: transparent;
+}
+
 /* Pullquote */
 
 .wp-block-pullquote {
Index: src/wp-content/themes/twentysixteen/css/editor-blocks.css
===================================================================
--- src/wp-content/themes/twentysixteen/css/editor-blocks.css	(revision 58196)
+++ src/wp-content/themes/twentysixteen/css/editor-blocks.css	(working copy)
@@ -416,6 +416,10 @@
 	background-color: #d1d1d1;
 }
 
+.wp-block-code.has-background code {
+	background-color: transparent;
+}
+
 /* Classic */
 
 .wp-block-freeform.block-library-rich-text__tinymce blockquote {