Welcome to the wonderful world of Magento, this won't be your first headache :)
The thing that makes Magento so powerful and also so difficult is that the system is designed to allow modifications at various places. The tricky part is finding where to customization was made. My guess is that this is actually not a custom option but a regular attribute? Otherwise you could just remove it at product management? So in case this is a regular attribute (you could see that by the CSS classes in HTML)
Usually "product attributes" are defined under Catalog > .... Attributes (srry, Magento's been a while) in the backend. Here you will find "attributes" and "attribute sets". Usually an attribute like above is linked to a product by it's attribute set. The set defines which attributes a type of product should have like color or size.
The second option is defining an attribute at product level like you did using a custom option. My guess is that this is an attribute, otherwise you would've seen it next to your custom option. You should also read into "product types (simple/configurable/grouped/etc...)" to get some understanding of this.
For now I think this is a product attribute but that's a problem because if you remove that, you will remove it for all the products in the same attribute set. It's really important tot define proper attributes/attribute sets at the start to prevent this problem. If you cannot remove the attribute because of what I just said, the product is probably configured with a wrong attribute set. You will have to recreate the product under a correct attribute set to solve this.
Default Magento does not allow a product to switch attribute sets but there are extensions that allow you to do this, at your own risk though.
If you're getting confused by the terms attributes, attributes sets, product types, layered navigation & custom options I actually recommend you to install a new store somewhere together with the sample data and read through some documentation related to these keywords. It's essential to understand.
If I misinterpreted your question, could you be so kind to be a little more detailed in your question? The more info about your situation, the more accurate I'm able to answer or suggest solutions.