Issues with automatic tracing of test cases

Try wrapping the existing logic in a conditional that returns null when the verification method is Design Review:

yourCustomFieldPropertyNameForVerificationMethod is NOT "Design Review" ? distinct(downstreamReferences(this).trackerTypes("testcase").{item|item.customField[5]} != ""
      ? downstreamReferences(this).trackerTypes("testcase").{item|item.customField[5]} : null)
  : null

An important note, choice fields in Codebeamer behave as collections even when single-select, so you usually can't compare them to a string directly — you compare against the option name, e.g. something like !this.customField[N].name.contains("Design Review") or by the option ID, depending on how that field is set up. That's the one piece worth testing carefully.

Also, after editing the formula, add Verification Method to the field's Compute dependencies so the TestCaseID value recomputes whenever the verification method changes.