diff --git a/x-pack/plugins/upgrade_assistant/server/lib/reindexing/reindex_service.test.ts b/x-pack/plugins/upgrade_assistant/server/lib/reindexing/reindex_service.test.ts
index e160ac37a9e3..44aed05b2c82 100644
--- a/x-pack/plugins/upgrade_assistant/server/lib/reindexing/reindex_service.test.ts
+++ b/x-pack/plugins/upgrade_assistant/server/lib/reindexing/reindex_service.test.ts
@@ -26,7 +26,6 @@ import { esIndicesStateCheck } from '../es_indices_state_check';
 import { versionService } from '../version';
 
 import { ReindexService, reindexServiceFactory } from './reindex_service';
-import { error } from './error';
 
 const asApiResponse = <T>(body: T): TransportResult<T> =>
   ({
@@ -638,12 +637,7 @@ describe('reindexService', () => {
             index: '.tasks',
             id: 'xyz',
           });
-          expect(log.warn).toHaveBeenCalledTimes(1);
-          expect(log.warn).toHaveBeenCalledWith(
-            error.reindexTaskCannotBeDeleted(
-              `Could not delete reindexing task xyz, got response "!?"`
-            )
-          );
+          expect(log.warn).toHaveBeenCalledTimes(0); // Do not log anything in this case
         });
 
         it('does not throw if task doc deletion throws', async () => {
@@ -672,6 +666,32 @@ describe('reindexService', () => {
           expect(log.warn).toHaveBeenCalledTimes(1);
           expect(log.warn).toHaveBeenCalledWith(new Error('FAILED!'));
         });
+
+        it.each([401, 403])(
+          'does not throw if task doc deletion throws AND does not log due to missing access permission: %d',
+          async (statusCode) => {
+            clusterClient.asCurrentUser.tasks.get.mockResponseOnce({
+              completed: true,
+              // @ts-expect-error not full interface
+              task: { status: { created: 100, total: 100 } },
+            });
+
+            clusterClient.asCurrentUser.count.mockResponseOnce(
+              // @ts-expect-error not full interface
+              {
+                count: 100,
+              }
+            );
+            const e = new Error();
+            Object.defineProperty(e, 'statusCode', { value: statusCode });
+            clusterClient.asCurrentUser.delete.mockRejectedValue(e);
+
+            const updatedOp = await service.processNextStep(reindexOp);
+            expect(updatedOp.attributes.lastCompletedStep).toEqual(ReindexStep.reindexCompleted);
+            expect(updatedOp.attributes.reindexTaskPercComplete).toEqual(1);
+            expect(log.warn).toHaveBeenCalledTimes(0);
+          }
+        );
       });
 
       describe('reindex task is cancelled', () => {
diff --git a/x-pack/plugins/upgrade_assistant/server/lib/reindexing/reindex_service.ts b/x-pack/plugins/upgrade_assistant/server/lib/reindexing/reindex_service.ts
index ce1f19f6babb..e55b4fce2e4d 100644
--- a/x-pack/plugins/upgrade_assistant/server/lib/reindexing/reindex_service.ts
+++ b/x-pack/plugins/upgrade_assistant/server/lib/reindexing/reindex_service.ts
@@ -309,20 +309,17 @@ export const reindexServiceFactory = (
     }
 
     try {
-      // Delete the task from ES .tasks index
-      const deleteTaskResp = await esClient.delete({
+      // Best effort, delete the task from ES .tasks index...
+      await esClient.delete({
         index: '.tasks',
         id: taskId,
       });
-      if (deleteTaskResp.result !== 'deleted') {
-        log.warn(
-          error.reindexTaskCannotBeDeleted(
-            `Could not delete reindexing task ${taskId}, got response "${deleteTaskResp.result}"`
-          )
-        );
-      }
     } catch (e) {
-      log.warn(e);
+      // We explicitly ignore authz related error codes bc we expect this to be
+      // very common when deleting from .tasks
+      if (e?.statusCode !== 401 && e?.statusCode !== 403) {
+        log.warn(e);
+      }
     }
 
     return reindexOp;