I went into Settings - Signature, deleted that message, replaced it with my name, and saved.
Now the signature on my outgoing mail is my name followed by "Get Outlook for Android."
The ad appears after I send the message, so I can't delete it before sending. A recipient pointed it out to me. Gratuitously pasting in ads on the sly after the user tries to get rid of them is truly tacky. If I can't get rid of the ad, I'll get rid of Outlook for Android.