We need to note few things about the scenario which will help us in reaching the correct solution.
Point 1 : The APIs are all publicly available and are associated with several mobile applications and web applications. This means Apply an IP blacklist policy is not viable option. as blacklisting IPs is limited to partial web traffic. It can't be useful for traffic from mobile application Point 2 : The organization does NOT want to use any authentication or compliance policies for these APIs. This means we can not apply HTTPS mutual authentication scheme.
Header injection or removal will not help the purpose.
By its nature, JSON is vulnerable to JavaScript injection. When you parse the JSON object, the malicious code inflicts its damages. An inordinate increase in the size and depth of the JSON payload can indicate injection. Applying the JSON threat protection policy can limit the size of your JSON payload and thwart recursive additions to the JSON hierarchy.
Hence correct answer is Apply a JSON threat protection policy to all APIs to detect potential threat vectors