I don’t use Mailchimp, but Sendy. Sendy have been making changes to the way third party signup methods work, they need to now include the list name and the account API.
Perhaps MC is the same now? If so, you need to add a hidden field to the form that is sent to MC to include this info.
For instance, again using Sendy as the example, you now need a hidden input field called list
with a list ID as the input and another called API
with your account API as the input.
It might be worth checking this in Post Office (which is very good) before looking for an alternative.
Failing that, some form stacks allow the addition of hidden fields and can send the inputs to a URL. The form stack in the UIkit framework can connect to Mailchimp and Sendy no bother, so that might be an option, although of course it might mean a rebuild on the site!
Failing that, and most likely the easiest option, is to just add some styling via CSS to the Mailchimp supplied signup box. If you post the code they’ve given you (remove private data) I’m sure people here can help with some simple CSS.