You don't need the "did" when it's the subject of the sentence.
Jeanne picked up a pen from the table and used it to sign the letter.
Who picked up the pen? -- No did. Subject.
What did she pick up? -- Did, direct object.
Where did she get the pen? -- etc.
What did she use to sign the letter?
What did she sign?
You CAN use the "did" to be emphatic.
Mark said it.
No, it wasn't mark.
The Peter said it?
No, it wasn't Peter either.
Then it must have been Mary.
No, Mary would never say such a thing.
Then who DID say it?
Student or Learner