diff --git a/homeassistant/components/synology_dsm/backup.py b/homeassistant/components/synology_dsm/backup.py
index 62a1b97b717..5f3312717ef 100644
--- a/homeassistant/components/synology_dsm/backup.py
+++ b/homeassistant/components/synology_dsm/backup.py
@@ -161,15 +161,20 @@ class SynologyDSMBackupAgent(BackupAgent):
 
         :param backup_id: The ID of the backup that was returned in async_list_backups.
         """
-        try:
-            await self._file_station.delete_file(
-                path=self.path, filename=f"{backup_id}.tar"
-            )
-            await self._file_station.delete_file(
-                path=self.path, filename=f"{backup_id}_meta.json"
-            )
-        except SynologyDSMAPIErrorException as err:
-            raise BackupAgentError("Failed to delete the backup") from err
+        for filename in (f"{backup_id}.tar", f"{backup_id}_meta.json"):
+            try:
+                await self._file_station.delete_file(path=self.path, filename=filename)
+            except SynologyDSMAPIErrorException as err:
+                err_args: dict = err.args[0]
+                if int(err_args.get("code", 0)) != 900 or (
+                    (err_details := err_args.get("details")) is not None
+                    and isinstance(err_details, list)
+                    and isinstance(err_details[0], dict)
+                    and int(err_details[0].get("code", 0))
+                    != 408  # No such file or directory
+                ):
+                    LOGGER.error("Failed to delete backup: %s", err)
+                    raise BackupAgentError("Failed to delete backup") from err
 
     async def async_list_backups(self, **kwargs: Any) -> list[AgentBackup]:
         """List backups."""
diff --git a/tests/components/synology_dsm/test_backup.py b/tests/components/synology_dsm/test_backup.py
index cdbc5934c5f..bcd9f1aa4eb 100644
--- a/tests/components/synology_dsm/test_backup.py
+++ b/tests/components/synology_dsm/test_backup.py
@@ -673,7 +673,11 @@ async def test_agents_delete_not_existing(
     backup_id = "ef34ab12"
 
     setup_dsm_with_filestation.file.delete_file = AsyncMock(
-        side_effect=SynologyDSMAPIErrorException("api", "404", "not found")
+        side_effect=SynologyDSMAPIErrorException(
+            "api",
+            "900",
+            [{"code": 408, "path": f"/ha_backup/my_backup_path/{backup_id}.tar"}],
+        )
     )
 
     await client.send_json_auto_id(
@@ -685,26 +689,40 @@ async def test_agents_delete_not_existing(
     response = await client.receive_json()
 
     assert response["success"]
-    assert response["result"] == {
-        "agent_errors": {
-            "synology_dsm.mocked_syno_dsm_entry": "Failed to delete the backup"
-        }
-    }
+    assert response["result"] == {"agent_errors": {}}
 
 
+@pytest.mark.parametrize(
+    ("error", "expected_log"),
+    [
+        (
+            SynologyDSMAPIErrorException("api", "100", "Unknown error"),
+            "{'api': 'api', 'code': '100', 'reason': 'Unknown', 'details': 'Unknown error'}",
+        ),
+        (
+            SynologyDSMAPIErrorException("api", "900", [{"code": 407}]),
+            "{'api': 'api', 'code': '900', 'reason': 'Unknown', 'details': [{'code': 407}]",
+        ),
+        (
+            SynologyDSMAPIErrorException("api", "900", [{"code": 417}]),
+            "{'api': 'api', 'code': '900', 'reason': 'Unknown', 'details': [{'code': 417}]",
+        ),
+    ],
+)
 async def test_agents_delete_error(
     hass: HomeAssistant,
     hass_ws_client: WebSocketGenerator,
+    caplog: pytest.LogCaptureFixture,
     setup_dsm_with_filestation: MagicMock,
+    error: SynologyDSMAPIErrorException,
+    expected_log: str,
 ) -> None:
     """Test error while delete backup."""
     client = await hass_ws_client(hass)
 
     # error while delete
     backup_id = "abcd12ef"
-    setup_dsm_with_filestation.file.delete_file.side_effect = (
-        SynologyDSMAPIErrorException("api", "404", "not found")
-    )
+    setup_dsm_with_filestation.file.delete_file.side_effect = error
     await client.send_json_auto_id(
         {
             "type": "backup/delete",
@@ -716,9 +734,10 @@ async def test_agents_delete_error(
     assert response["success"]
     assert response["result"] == {
         "agent_errors": {
-            "synology_dsm.mocked_syno_dsm_entry": "Failed to delete the backup"
+            "synology_dsm.mocked_syno_dsm_entry": "Failed to delete backup"
         }
     }
+    assert f"Failed to delete backup: {expected_log}" in caplog.text
     mock: AsyncMock = setup_dsm_with_filestation.file.delete_file
     assert len(mock.mock_calls) == 1
     assert mock.call_args_list[0].kwargs["filename"] == "abcd12ef.tar"