As a former realtor, there are several mistakes with your question:
1. Your statement "My agent told me that once escrow closes and they give me the check back, I have to go cash it and give her $3,000. because she is saying that she put that amount (as a favor) towards escrow."
In the sentence above you indicate this agent is working for your parents who was waiting for a sale to close. If your parents are the clients, no agent will talk to you or get you involved with escrow, checks, etc. This is between your parents and their agent. The exception is if your parents are not coherent and you have a Power or Attorney to act on their behalf to buy a home. With a Power of Attorney signed, then your parents agent will work with you.
2. When buyers purchase a home, any money deposited into an escrow account must be kept separate from other funds and is documented. As buyers, you should get a receipt with the amount deposited, financial institution and account number. If you did not get a receipt, this is fraud.
3. On the closing documents, it will state all amounts deposited / down payment and all credits applied. It will list items paid - taxes, insurance, fees, etc. An agent can give a rebate to their buyer clients but this is AFTER closing and is separate from the real estate transaction. Not all states allow this and not all agents do this. If the agent wants to give a rebate, the money will be from their personal account - not from the escrow account or from the real estate transaction. Most likely the agent's rebate will be from their commission paid.
4. If an agent tells you something different than #3 - such as the $3,000. has to do with escrow, this is fraud and you need to report this to a real estate attorney.