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.
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.