Use a split toggle button to reflect scaling state.

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

 {
   "ACCESS_CODE": {
     "message": "Access code",
     "description": "Label for the access code entry box. This is where the client user enters the code that permits access to the host."
   },
   "ACCESS_CODE_TIMER": {
     "message": "This access code will expire in $timeout$",
     "description": "Text displayed when the access code is due to time out within 30 seconds.",
     "placeholders": {
       "timeout": {
@@ skipping 169 matching lines @@
     "description": "Web-app description. Displayed in Chrome's extensions page."
   },
   "PRODUCT_NAME": {
     "message": "Chromoting",
     "description": "The product name. Displayed in various Chrome page, including the New Tab page, and displayed prominently on the app's main page."
   },
   "PRODUCT_NAME_AND_VERSION": {
     "message": "Chromoting v1.0",
     "description": "The product name and version number. Displayed in Chrome's extensions page."
   },
-  "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."
   },
   "STOP_SHARING_BUTTON": {
     "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."
   }
 }