Hey there @Dunjoko -- great question!
You will not want to accept the invitation that they sent you unless you plan to be a user within their Calendly organization. This would mean you would fall under their billing plan, and that they would have owner/admin privileges over your account. If this is not your intention, do not accept the invite. If you have already accepted the invite, they are going to have to remove you from their organization. This invite and becoming a user within their organization will not give you the access that you were looking for.
The only way to achieve what you are looking to do is to log into their account with their credentials. This means they will need to provide you their username and password.
I hope this helps!