Do I need to wash my extensions after curling to make them straight again?

No, unless the extensions have a lot of product buildup (like hairspray), this is not needed. Instead, you can gently brush out the curls with a soft bristle brush from bottom to top, and use a hair straightener to straighten the extensions. Be sure to use a heat protectant spray prior to straightening, and to use a low to medium heat setting. Keep in mind, using sticky products such as hairspray, hair gel, or hair wax, can and likely will clog up your extensions. The more products you use, the more you will need to wash your extensions, leading to dry, tangled extensions. Also, keep in mind that any products that you use on your natural hair can transfer onto your extensions.