Probably she asked for some kind of registered delivery, someone asked her, "what are the contents worth?", in order to get a number to put into the insurance calculator, and she said "$60000".
If that's true, meaning that if the letter goes astray, you can't get a new one issued, then yes you should insure it to the value of $60000 (or rather, since the insurance is so much, you should not post it at all. Your girlfriend could perhaps return it to her client and agree with them another way to transfer money). I'm also not sure what happens when a letter hits US customs with a declared value of $60000!
However, it's probably not true. This is a check (or, if drawn on a bank here in the UK, a cheque), not a bearer bond. If it goes missing then (with some trouble and expense) she can almost certainly get another one issued. So the correct answer to "what's this worth?" is the cost of replacing it, not the amount of money that it instructs the bank to transfer.
As for whether it'll cause a red flag for you, I'm afraid I don't know enough about US banking to say. Here in the UK there should be no problem with a cheque for that amount, unless one of the banks involved has reason to suspect money laundering or related financial crime, in which case they're required to report it. But if the cheque is from a non-US account and you're paying it into your US account, then maybe you need to make a customs declaration?