<apex:column > <apex:commandLink action="{!deleteItem}" reRender="frmList"  oncomplete="updateCarts();"> Remove</apex:commandLink></apex:column>

<script>      
         function updateCarts(){  
            var listId = "{!ids}";
             alert(listId);
            
        } 
        </script>

public string ids { get; set;}
public CartsController()
  { 
   ids= 'ABCDEF';   
  }
  public void deleteItem()
  {
    ids='123456';
  }