I agree with Gary's comments. If you really want to move, work out your differences, agree on terms and get the house sold. In this buyers market just getting an offer is wonderful. You might not get another for a long time.
I am a licensed agent in both Michigan and Florida.

Cheryl, Just to ask, how long was your home on the market before receiving this offer? Many homes in southeastern Michigan have and are continuing to decline in value. Do you believe that the next buyers appraiser will determine your home is worth more? Were there unsimilar homes in the appraisal?

I suggest sitting down with your agent, and as others have expressed the broker/owner and get this straightened out to your satisfaction. Please review your listing contract, most have specific clauses near the begining as to what the agent and broker must do.

I wish you luck, please let us know how this ends.

Of there are no initials by the whited out new terrms you do not have a valid offer. Call the Broker of the your agent, if he is doesn't handle it, call an attorney and give show him contract, not signed by you. When you verbally countered did you say yes. Why would the buyers agent do this? Even if you said yes, and had 2nd thoughts but did not sign it you should be able to get out of it as all contracts in real estate must be in writing.

An oral offer is worth the paper it's written on...worthless.
Any time you deal with anything of value, the rule is put it in writing.
When a property appraises less than the purchase price, usually that means either the seller lowers the price, the buyer antes up more down payment, or a meeting in the middle.

I would be inclined to work with the buyer....maybe discuss with your Realtor's broker. I am concerned about some othe comments you made, particularly the fact your agent orally presented an offer. "Verbally" could mean written, emailed, spoken...it means with VERBS. Oral means spoken written means...IN WRITING

A real estate contract in Michigan needs to be in writing. If you don't have a contract in writing you don't have an agreement. You are most likely out, though I would suggest you speak with your agent's managing broker if your agent is not delivering your rejection. A real estate attorney could be your next step after the broker.