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The travel expenses is "reimbursement" for your actual expenses - you are not required to return that money.
I would strongly encourage you to contact a local employment law attorney (even if you are not planning on filing a claim, it is well worth at least making a phone call - before you take any action, such as giving notice - to discuss your situation with a local attorney in more detail and consider whether or not it is worth pursuing action).
Being in a hostile work environment makes it very difficult to process these matters clearly, and it is worth speaking with a lawyer early on in the process (before you separate) to discuss the matter. You may not feel like suing the company now, but preserving any potential cause of action will be invaluable later (if you change your mind).
(Again, speaking to a local attorney now does not obligate you to any course of action, and it is covered by the attorney/client relationship - so anything you speak to this attorney about will not be subject to anyone else finding out).
You can find local attorneys using the State and local Bar Association directories, or private directories such as www.AVVO.com; www.FindLaw.com; or www.Martindale.com (I personally find www.AVVO.com to be the most user friendly).