Here is a possible (albeit perhaps not too elegant) solution.
Insert in the header a code like that
// badheader.hpp
namespace {
[[deprecated("This header is deprecated")]]
constexpr static int badheader_hpp_is_deprecated = 0;
constexpr static int please_dont_use_badheader_hpp = badheader_hpp_is_deprecated;
}
This creates a deprecated variable badheader_hpp_is_deprecated. The initialization of please_dont_use_badheader_hpp triggers the deprecated warning. Notice that I put both variables inside an anonymous namespace, to avoid possible name conflicts.
Still, as noted in the comment, a name clash could still happen if, in the same compilation unit, a variable with the same name is declared inside the anonymous namespace. For this reason, as suggested in the comments, variables in the code above have a descriptive name, rendering name clash high improbable.