Something that's trumped-up is faked or fabricated to use as an excuse. You might be tempted to tell your parents a trumped-up story about a mean math teacher to explain a bad grade.
When you hear about someone being arrested on "trumped-up charges," that means that they've been falsely accused. There's a sense of exaggeration in this term, as well—if your excuse for being late is trumped-up, you're concocting extra details to make it sound more impressive. Trumped-up was first recorded in the early 18th century, and it comes from the idiomatic trump up, "devise deceitfully or dishonestly."