Is there a way to let user add and remove fields with Contact Form 7? [closed]

If you know enough about php, jquery and css, you can use shortcode in contactform 7, this plugin bring ability to integrate a shortcode inside your contact form, then you can write that shortcode with any functionality you like.

I recommend to add a filter in your shortcode and then by using metabox make your desired field and finally add the shortcode to your contact form.