Left signature question on 1911 and 1917 DOC $1 notes

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I have been expanding my collection into DOC notes.  I've noticed that on the 1911 and 1917 $1 notes in particular (perhaps others), that some available notes have a left counter signature, while other notes do not.

According to Charleton, the left manuscript counter signatures were to be by various Finance Department employees.

My question; is there a difference in value (or collect-ability) between notes with a left counter signature vs. notes without a signature?

Perhaps someone could clarify this for me.

Notes without any left signature at all have very likely been washed and/or bleached in a sad effort to make them look nicer, resulting in the loss of the manuscript signature.  Some advanced collectors consider such notes to be ruined and do not want them at any price.  Novice collectors might be taken in by them.