There is no Call to "remove Cart item" if that is what you asking for.
When you want to delete an item of the cart, you need to know the current status of the cart and remove the particular item you want to remove and then send that data with the usual trackcart call. And you really need to implement the uniquevalue for the customer called "email".
Here an Example Payload that gets transferred when you perform the call:
payload: {"cart":[{"item":"ProductNumber","quantity":"1"},{"item":"ProductNumber","quantity":"1"}],"url":"https://www.XXX.eu/","user_info":{"email":"UniqueCustomerValue"}}
Result after you remove one Item:
payload: {"cart":[{"item":"ProductNumber","quantity":"1"}],"url":"https://www.XXX.eu/","user_info":{"email":"UniqueCustomerValue"}}
Currently your questions tries to communicate a solution but you should rather show your use case and not a solution you may got for this usecase. This is a common problem called XY problem.
Maybe your question leads to: How can i make sure that an item won't show up in recommendations?
If you want to make a product unavailable just set the OnlineAvailability flag to No. Setting this will automatically remove the product out of every recommendation.