#1 Remember that individual states have different regulations about how real estate sales are handled, and some things that are legal and acceptable in one state might not be in another.
If the bank owns the property, they can accept or refuse any offer that they receive! - just as you can when you have an item you want to sell. They are making business decisions based on what they feel is in their best interests. That being said, (in Pennsylvania) a verbal contract for the sale of real estate is legal- it just may not be enforceable. Some banks have a practice of taking the offers as they come in, and only look at one at a time, playing it out to the end before they even look at the next offer. Other institutions look at everything that comes in by a certain cut-off date, considering them all at the same time. Banks are not generally in the business of holding and paying utilities on vacant properties, and want to sell them quickly. But they also want to NOT lose money!.
Ask the agent you are working with what the rules are.
Now you need to decide if you are willing to agree to the counter offer-verbal or otherwise. Does the counter offer they are making still make financial sense to you.
Hope you make a good profitable decision!