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A restraining order against you is a very significant issue (it prohibits you from owning firearms, it shows up on background checks, it will appear in future court proceedings (even if you don't anticipate any now)).
If it is a weak application, show up and defend yourself, and defeat the petition.
You can of course file your own restraining order against her, but frankly filing a second frivolous petition is likely to make matters worse, not better.
Writing a letter is not a proper response.
If you cannot appear, write a formal "Opposition" and file it with the court, and serve a copy on the petitioner (have a third party send it to them via USPS, and file a "proof of service" with the court along with your opposition).
In your Opposition, show that there is no credible evidence that you showed any threat to this individual.
You should file an opposition even if you appear in court.
(However, this is a very serious issue, if you cannot take the time off work, hire a lawyer to go for you. This really is the type of thing you take time off work for!!!).
Make sure you get it filed. You can send a "courtesy copy" to the judge as well.
You can have a copy faxed, emailed, or hand delivered to the applicant. (The whole idea is to ensure that you aren't engaging in "ex parte" communications with the court - where you are sending something to the court without showing the other party).