Fetch a new GAIA picture every time chrome://settings/manageProfile comes up.

chrome/browser/resources/options/browser_options_profile_list.js

Index: chrome/browser/resources/options/browser_options_profile_list.js
diff --git a/chrome/browser/resources/options/browser_options_profile_list.js b/chrome/browser/resources/options/browser_options_profile_list.js
index 429780ede632a32dc16a9296bc2d735e7b39a452..b995ca0946b2ef57c0d5b6f5c78baa981e3397e5 100644
--- a/chrome/browser/resources/options/browser_options_profile_list.js
+++ b/chrome/browser/resources/options/browser_options_profile_list.js
@@ -117,8 +117,10 @@ cr.define('options.browser_options', function() {
     activateItemAtIndex: function(index) {
       // Don't allow the user to edit a profile that is not current.
       var profileInfo = this.dataModel.item(index);
-      if (profileInfo.isCurrentProfile)
+      if (profileInfo.isCurrentProfile) {
+        chrome.send('refreshGAIAPicture');
         ManageProfileOverlay.showManageDialog(profileInfo);
+      }
     },
 
     /**