Agreed. Especially as I'd like to see us improve the deletion experience at some point.

Change should go into
components/omnibox/browser/base_search_provider.cc

It should only be landed after
https://chromium-review.googlesource.com/c/chromium/src/+/1050465
has landed, which converts the deletion URL fetcher to use the new network interface.

It should look something like
  // Note: It's OK to pass SignedIn::kNo if it's unknown, as it does not affect
  // transmission of experiments coming from the variations server.
  variations::AppendVariationHeaders(
      request->url,
      client()->IsOffTheRecord() ? variations::InIncognito::kYes
                                 : variations::InIncognito::kNo,
      variations::SignedIn::kNo, &request->headers);

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/abc13a1c70aff0593c3e6e30e8f8645eda53f2a8

commit abc13a1c70aff0593c3e6e30e8f8645eda53f2a8
Author: Mark Pearson <mpearson@chromium.org>
Date: Wed Jun 27 20:06:14 2018

Omnibox - Append Variation Headers on Suggest Deletion Requests

These are requests to delete a personalized query suggestion that
came from Google's servers.

Tested by looking for X-Chrome-Data header using about:net-internals
before and after this change on the delete request.

Bug:  848992 
Change-Id: I900b80891fde655d87c88d2de060728d976688b2
Reviewed-on: https://chromium-review.googlesource.com/1105463
Reviewed-by: Justin Donnelly <jdonnelly@chromium.org>
Commit-Queue: Mark Pearson <mpearson@chromium.org>
Cr-Commit-Position: refs/heads/master@{#570878}
[modify] https://crrev.com/abc13a1c70aff0593c3e6e30e8f8645eda53f2a8/components/omnibox/browser/base_search_provider.cc