Employment Law Questions? Ask an Employment Lawyer.
That will depend on how your employer took it, and relates to what you said and the tone you used. It is not unreasonable for an employer to consider that a rude or disrespectful remark.
Of course, employment law doesn't define what rude or disrespectful means. The employer has the legal ability to define that for themselves.
If the employer here decides it was rude, whether I would agree or not isn't the issue. What matters then is what the employer can do about it and that will depend on what type of employee you are. If you have no employment contract specifically stating that you can only be terminated for cause, you are an "at will" employee and can legally be terminated at any time, with or without cause. In that situation, the employer could decide this was rude and whatever action they chose (up to and including termination).
I can't tell you if it will cause some action. Employers have the independent ability to decide what action they will or will not take.
If you don't have a contract of employment like the one I mentioned, then no they don't have to give warning first.
They can fire you for that, because legally they don't even need a reason to terminate you.
She can wait for the appropriate time. Again, this is "at will" employment we're talking about. There are not any sort of strict rules about when, how and why they can terminate.
An employment contract is with an individual. You would know if you had that contract.
USPS may have a collective bargaining agreement though, so if you are union you'd have some more protections, but would have to go through your union rep.
There may be a requirement for warnings, etc. if you are in one of those protected positions, but these have to be discussed with your HR and/or union rep.
There is no external remedy. You need to go to your HR, or if you are union go to your union rep. Any rights that you have are internal to the employer here, because outside law gives you no protection on these facts.
If you have a right to a warning, it will be because the employer requires it through either their own policies or because the union collective bargaining agreement requires it.