Here is the updated color palette with Emerald Green removed:

{
  "palette_name": "Warm Earthy Tones",
  "colors": [
    {
      "name": "Warm Beige",
      "hex_code": "
                            
                            #E6D5C3
                        "
    },
    {
      "name": "Cocoa Brown",
      "hex_code": "
                            
                            #8B5E3C
                        "
    },
    {
      "name": "Sage Green",
      "hex_code": "
                            
                            #A6B17E
                        "
    },
    {
      "name": "Berry Pink",
      "hex_code": "
                            
                            #D6396D
                        "
    },
    {
      "name": "Dusty Rose",
      "hex_code": "
                            
                            #D8A39E
                        "
    },
    {
      "name": "Vibrant Teal",
      "hex_code": "
                            
                            #008080
                        "
    }
  ]
}

This palette retains a warm and inviting feel with rich earth tones and a pop of color from the vibrant teal. If you need any further modifications or assistance, just let me know!