http2: do not modify explicity set date headers

Fixes: nodejs#30894
Refs: nodejs#29829

lib/internal/http2/core.js

@@ -2234,7 +2234,10 @@ function processHeaders(oldHeaders) {
   const statusCode =
     headers[HTTP2_HEADER_STATUS] =
       headers[HTTP2_HEADER_STATUS] | 0 || HTTP_STATUS_OK;
-  headers[HTTP2_HEADER_DATE] = utcDate();
+
+  if (headers[HTTP2_HEADER_DATE] === null ||
+      headers[HTTP2_HEADER_DATE] === undefined)
+    headers[HTTP2_HEADER_DATE] = utcDate();
 
   // This is intentionally stricter than the HTTP/1 implementation, which
   // allows values between 100 and 999 (inclusive) in order to allow for

test/parallel/test-http2-removed-header-stays-removed.js

@@ -0,0 +1,43 @@
+// Copyright Joyent, Inc. and other Node contributors.
+//
+// Permission is hereby granted, free of charge, to any person obtaining a
+// copy of this software and associated documentation files (the
+// "Software"), to deal in the Software without restriction, including
+// without limitation the rights to use, copy, modify, merge, publish,
+// distribute, sublicense, and/or sell copies of the Software, and to permit
+// persons to whom the Software is furnished to do so, subject to the
+// following conditions:
+//
+// The above copyright notice and this permission notice shall be included
+// in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
+// NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+// DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
+// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
+// USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+'use strict';
+const common = require('../common');
+if (!common.hasCrypto) { common.skip('missing crypto'); }
+const assert = require('assert');
+const http2 = require('http2');
+
+const server = http2.createServer(common.mustCall(function(request, response) {
+  response.setHeader('date', 'snacks o clock');
+  response.end();
+}));
+
+server.listen(0, common.mustCall(function() {
+  const session = http2.connect(`http://localhost:${server.address().port}`);
+  const req = session.request();
+  req.on('response', function(headers, flags) {
+    assert.deepStrictEqual(headers.date, 'snacks o clock');
+  });
+  req.on('end', function() {
+    session.close();
+    server.close();
+  });
+}));