Removing the date of birth field from the PrestaShop 1.7 registration form is, like removing the Company name, a simple and quick fix.
In the admin panel of your PrestaShop store, in the Configure section, select Shop Parameters and then Customer Settings. In the Customer Settings tab, you will have the general settings for the registration form.
In the field Ask for birth date, move the slider to No position and you're done.
Remember to save the change.
Other articles about the registration form in PrestaShop 1.7: