diff --git a/meta-gnome/recipes-gnome/mutter/mutter/0001-cogl-Fix-GLES2-fallback.patch b/meta-gnome/recipes-gnome/mutter/mutter/0001-cogl-Fix-GLES2-fallback.patch
deleted file mode 100644
index ec92000424..0000000000
--- a/meta-gnome/recipes-gnome/mutter/mutter/0001-cogl-Fix-GLES2-fallback.patch
+++ /dev/null
@@ -1,37 +0,0 @@
-From f4f7e31303d78b2a8a0881b61311b8d750301b8f Mon Sep 17 00:00:00 2001
-From: Adam Jackson <ajax@redhat.com>
-Date: Tue, 29 Oct 2019 11:53:27 -0400
-Subject: [PATCH] cogl: Fix GLES2 fallback
-
-Say you're using intel gen3, you poor soul. Your big-GL maxes out at 1.5
-unless you use dirty tricks, but you do have GLES2. We try to fall back
-to GLES in this case, but we only ever say eglBindAPI(EGL_OPENGL_API).
-So when we go to do CreateContext, even though we think we've requested
-GLES 2.0, the driver will compare that "2.0" against the maximum big-GL
-version, and things will fail.
-
-Fix this by binding EGL_OPENGL_ES_API before trying a GLES context.
-
-https://gitlab.gnome.org/GNOME/mutter/issues/635
-
-Upstream-Status: Applied
----
- cogl/cogl/winsys/cogl-winsys-egl.c | 2 ++
- 1 file changed, 2 insertions(+)
-
-diff --git a/cogl/cogl/winsys/cogl-winsys-egl.c b/cogl/cogl/winsys/cogl-winsys-egl.c
-index 99dcb8bf3..f2b439a67 100644
---- a/cogl/cogl/winsys/cogl-winsys-egl.c
-+++ b/cogl/cogl/winsys/cogl-winsys-egl.c
-@@ -329,6 +329,8 @@ try_create_context (CoglDisplay *display,
-   if (renderer->driver == COGL_DRIVER_GL ||
-       renderer->driver == COGL_DRIVER_GL3)
-     eglBindAPI (EGL_OPENGL_API);
-+  else if (renderer->driver == COGL_DRIVER_GLES2)
-+    eglBindAPI (EGL_OPENGL_ES_API);
- 
-   egl_attributes_from_framebuffer_config (display,
-                                           &display->onscreen_template->config,
--- 
-2.21.0
-
diff --git a/meta-gnome/recipes-gnome/mutter/mutter_3.34.3.bb b/meta-gnome/recipes-gnome/mutter/mutter_3.34.4.bb
similarity index 93%
rename from meta-gnome/recipes-gnome/mutter/mutter_3.34.3.bb
rename to meta-gnome/recipes-gnome/mutter/mutter_3.34.4.bb
index 9afa269ed1..b4ddc5dadf 100644
--- a/meta-gnome/recipes-gnome/mutter/mutter_3.34.3.bb
+++ b/meta-gnome/recipes-gnome/mutter/mutter_3.34.4.bb
@@ -22,9 +22,8 @@ GNOMEBASEBUILDCLASS = "meson"
 
 inherit gnomebase gsettings gobject-introspection gettext upstream-version-is-even features_check
 
-SRC_URI[archive.md5sum] = "c3ee46ae7b84d9d0e8dd3f9e04a61ab1"
-SRC_URI[archive.sha256sum] = "cdf57ddd0bc35db952b732b77c796760e65d1ce2f7df31273e5c8d4759ed4a89"
-SRC_URI += "file://0001-cogl-Fix-GLES2-fallback.patch"
+SRC_URI[archive.md5sum] = "de19a6de98a2250dd7efdfca14359e39"
+SRC_URI[archive.sha256sum] = "0134513515f605dd0858154d0b54d2e23c5779d52590533e266d407251e20ba2"
 
 # x11 is still manadatory - see meson.build
 REQUIRED_DISTRO_FEATURES = "x11"