When you want to open a web site, your browser sends a so-called "GET request" to the server which contains then URL and some setting information like preferred language ans such. The server then answers this request by sending the web pages content. Or an error message like 404.
How about the part where you're being the client making a request to server of some service, but for some reason think you're the party that get's to have terms of service.
Any kind of agreement or contract has two sides. There is no reason not to add a X-TermsOfService parameter to a GET request. The Host will probably ignore it, but legally, you have made a contract offer, and by replying, the server implicitly agrees to it. How much this holds up in court is a different question, but if your TOS is reasonable, a judge might even lean in your favor. If a web site offers their TOS, it is not in any way different.