Technically if it was a 141 stage check it is not a "checkride".
An intermediate stage check is definately not a check ride, and you should not have to report that. Since 61 students don't even have stage checks it's not really fair that you should be penalized just because you did 141. Actually nobody cares about intermediate stage checks anyway.
However if you failed (or got an incomplete) on an end-of-course check that would have resulted in issuance of a certificate, you probably want to report that one, since that's really what they're asking.
However no 141 stage or end-of-course check failures should not appear in your FAA record (unless an outside DPE mistakenly issued a pink slip).