Yes, you can adjust the design of Sirvoy’s hotel booking engine to suit your website (which is especially handy if you use the iframe) by going to Settings -> Booking form -> Click Edit design for your booking form under Manage booking forms.
Here you can choose CSS which will give you the ability to customize all the aspects of the design. When using this option you will be able to take away elements from the booking form such as the flags or the copyright text. You will need some basic knowledge of CSS to use this option.
You can find more information about how to add Sirvoy’s booking form to your website on this support page.