Is there a way to avoid the advertising after the submission has been submitted?

I did a test submission and notice it then takes you to a "Thank you for your submission" page and has a link to JotForm's page. I understand the marketing aspect on JotForm's behalf, but I don't know that having "sign up! it's free!" really makes us look as professional as I was hoping to using the form for applicants.

The option to remove "Powered by Jotform" is available on paid plans. It can be removed under the Settings option of your form. There should be an option which is, JotForm branding, where you can disable the advertising. 

You could upgrade your account and un-check the JotForm branding option from "My Account Settings" page: 

This should remove the branding from the thank you page, please if you have any question, let us know.