Use a split toggle button to reflect scaling state.

remoting/webapp/me2mom/_locales/en/messages.json

Index: remoting/webapp/me2mom/_locales/en/messages.json
diff --git a/remoting/webapp/me2mom/_locales/en/messages.json b/remoting/webapp/me2mom/_locales/en/messages.json
index 8ea98780fd76c0d4f7f45eb189254f0c74f664b2..17bd133535a6347dd4a6b3fd784209cfbf3ecf16 100644
--- a/remoting/webapp/me2mom/_locales/en/messages.json
+++ b/remoting/webapp/me2mom/_locales/en/messages.json
@@ -197,10 +197,6 @@
       }
     }
   },
-  "SCALE_BUTTON": {
-    "message": "Fit Screen",
-    "description": "Label for the scaling button. Clicking this toggles between scale-to-fit and 1:1 mode. This is displayed in a tool-bar with limited horizontal space; please try to keep the translation under 20 characters."
-  },
   "SHARE_BUTTON": {
     "message": "Share This Computer",
     "description": "Label for the share button on the host-side. Clicking this button generates an access code to be conveyed to the client."
@@ -209,6 +205,10 @@
     "message": "Stop Sharing",
     "description": "Label for the 'stop sharing' button on the host-side. Clicking this button disconnects the client."
   },
+  "TOOLTIP_SCALING": {
+    "message": "Scale to fit",
+    "description": "The tool-tip shown when the user hovers over the scale to fit button. Clicking this button toggles between scaling down the remote desktop to fit it inside the Chromium browser window and displaying it at 1:1 scale."
+  },
   "VERIFYING_CODE": {
     "message": "Verifying access code…",
     "description": "Message displayed on the client while the access code is verified."