Sign it.

One year is nothing in aviation, especially when just starting to build time.
Small world, companies talk and also pay attention to resumes. A resume were someone stayed for short time at a company is raising questions and they want answers to why. Really it is not the end of the world, they are not out to get you, just protecting their investment.

In all honestly I don't get it why people make such a big deal about it. Be happy you have a job in these times.