Moreover, Howard-Snyder seems to assume
that truth-making is closed under logical
implication […] But that assumption is false. For example, “[a cat] has
retractable claws” implies that “Grass is green,” since both are true, but they
obviously have different truth-makers. (§3)

I have nothing to say about whether
truth-making is closed under logical implication. I do have something to say
about Craig’s argument that

*A * A cat has retractable claws.

(logically) implies

*B* Grass is green.

“Since”, Craig says, “both are true”.
Craig is almost certainly confused here.

By my lights, a
sentence/statement/proposition 𝒫* *logically implies 𝒬* *, abbreviated 𝒫 ⊨ 𝒬, just in case 𝒬 is a logical
consequence of 𝒫,
which is to say that there is no truth-value assignment or “valuation” in which
𝒫 is true and 𝒬 is false. But, if
you were to put *A* and *B* on a truth table, there will be one
line in which *A* is true and* B* is false. Hence A does not logically
imply B, or

*A*
⊭ *B*

It may be, however, that all that Craig
intended is to say is that, given that *A*
and *B* are true, *A* “materially” implies *B*,
or *A* ⊃
*B*. Indeed, since there is no truth
value assignment in which *A* and *B* are true and *A* ⊃
*B*
if false, the former logically implies the latter, or

*A* & *B* ⊨ *A* ⊃
*B*

Note, however, that this doesn’t affect
my previous point. It’s one thing to say that,

given *A* & *B*, the material conditional *A** *⊃ *B* is true,

and it’s another to say that,

given *A* & *B*, *A*
logically implies *B*.

The former says something true about
the conjunction, *A* & *B*, in relation to the material
conditional, *A* ⊃ *B*, whereas the latter says something
false about the conjunction, *A* & *B*, and its relation to another relation:
the relation between *A* and *B* per se.

Now, by my understanding,

Relation ℛ is *closed under logical implication* just in
case, if *x* stands in relation ℛ to 𝒫,
and if 𝒫
logically implies 𝒬,
that is 𝒫
⊨ 𝒬, then *x* stands in relation ℛ to 𝒬.

For example: some have thought, but
many deny, that the *knows that*
relation between an agent and a proposition is closed under logical
implication. This view has the consequence that, if Craig knows that *A*, then Craig knows that: either *A* or ¬*B*, for *A* ⊨ *A* v ¬*B*.
Notice that if the *knows that*
relation were closed under logical implication, and we understood logical
implication as “material” implication, then those who think that the *knows that* relation is closed under
logical implication would be saddled with the view that, if Craig knows *A*, then Craig knows *B*, for *A *⊃ *B*. As dubious as the view that the *knows that* relation is closed under
logical implication might be, it's not* that *dubious.

Similarly, if we suppose that the *makes true* relation is closed under
logical implication, then this would require only that, e.g., if *x* makes it true that *A*, then *x* makes it true that: either *A*
or ¬*B*, for again *A* ⊨ *A* v ¬*B*.
It would not require that, if *x* is makes it true that *A*, then *x* makes it true that *B*, as *A* ⊭ *B*, and this despite the fact that *A*
and *B* are both true. In summary,
then, it appears that Craig’s argument against the view that the *makes true* relation is closed under
logical implication rests upon the following false conditional: If *A* and *B*, then *A* logically
implies *B*.