Clean up deprecated Web Push API code-paths.

chrome/test/data/push_messaging/test.html

Index: chrome/test/data/push_messaging/test.html
diff --git a/chrome/test/data/push_messaging/test.html b/chrome/test/data/push_messaging/test.html
index 1a3bd65213324bd34421982620227f3d9f061647..19973cb8c91c00d9216f2a6739045e53e5215c59 100644
--- a/chrome/test/data/push_messaging/test.html
+++ b/chrome/test/data/push_messaging/test.html
@@ -24,8 +24,7 @@
 
     function registerPush() {
       navigator.serviceWorker.ready.then(function() {
-        // TODO(peter): Remove the argument once Blink no longer requires it.
-        navigator.push.register('DEPRECATED').then(function(pushRegistration) {
+        navigator.push.register().then(function(pushRegistration) {
           sendResultToTest(pushRegistration.pushEndpoint + ' - ' + pushRegistration.pushRegistrationId);
         }, sendErrorToTest);
       }, sendErrorToTest);