A textstraining order is similar to a restraining order that you apply for when you're having a disagreement with friends, enemies or your significant other. Although it covers only text messaging, it means that they are prohibited from sending you texts for the duration of the textstraining order. This usually occurs after a textmestic.
Jane showed me some texts that John sent her during a textmestic they were having. They were so bad that she applied for a textstraining order. That ought to keep his thumbs idle for a while.