diff --git a/src/ParallelAlgorithms/Interpolation/InterpolationTargetDetail.hpp b/src/ParallelAlgorithms/Interpolation/InterpolationTargetDetail.hpp
index 3ad7b5b2e4f8c..9e9b97637afc6 100644
--- a/src/ParallelAlgorithms/Interpolation/InterpolationTargetDetail.hpp
+++ b/src/ParallelAlgorithms/Interpolation/InterpolationTargetDetail.hpp
@@ -95,17 +95,6 @@ double get_temporal_id_value(const T& id) {
 }
 
 CREATE_IS_CALLABLE(apply)
-CREATE_IS_CALLABLE_V(apply)
-
-template <typename Callbacks, typename Box, typename Cache, typename TemporalId>
-struct AllSimpleCallbacks;
-
-template <typename... Callbacks, typename Box, typename Cache,
-          typename TemporalId>
-struct AllSimpleCallbacks<tmpl::list<Callbacks...>, Box, Cache, TemporalId>
-    : public std::integral_constant<
-          bool, tmpl2::flat_all_v<is_apply_callable_v<Callbacks, Box, Cache,
-                                                      TemporalId>...>> {};
 
 template <typename T, typename DbTags, typename Metavariables,
           typename TemporalId>
@@ -115,8 +104,10 @@ bool apply_callbacks(
     const TemporalId& temporal_id) {
   using callbacks = typename T::post_interpolation_callbacks;
   constexpr bool all_simple_callbacks =
-      AllSimpleCallbacks<callbacks, decltype(*box), decltype(*cache),
-                         decltype(temporal_id)>::value;
+      tmpl::all<callbacks,
+                is_apply_callable<tmpl::_1, tmpl::pin<decltype(*box)>,
+                                  tmpl::pin<decltype(*cache)>,
+                                  tmpl::pin<decltype(temporal_id)>>>::value;
   if constexpr (all_simple_callbacks) {
     tmpl::for_each<callbacks>([&](const auto callback_v) {
       using callback = tmpl::type_from<decltype(callback_v)>;
@@ -138,10 +129,10 @@ CREATE_HAS_STATIC_MEMBER_VARIABLE(fill_invalid_points_with)
 CREATE_HAS_STATIC_MEMBER_VARIABLE_V(fill_invalid_points_with)
 
 template <typename T, bool B>
-struct with_value;
+struct fill_value_or_no_such_type;
 
 template <typename T>
-struct with_value<T, false> {
+struct fill_value_or_no_such_type<T, false> {
   using type = NoSuchType;
 };
 
@@ -151,22 +142,21 @@ struct DoubleWrapper {
 };
 
 template <typename T>
-struct with_value<T, true> {
+struct fill_value_or_no_such_type<T, true> {
   using type = DoubleWrapper<T>;
 };
 
 template <typename Callback>
-struct get_value {
-  using type =
-      typename with_value<Callback,
-                          has_fill_invalid_points_with_v<Callback>>::type;
+struct get_fill_value {
+  using type = typename fill_value_or_no_such_type<
+      Callback, has_fill_invalid_points_with_v<Callback>>::type;
 };
 
 template <typename Callbacks>
 struct get_invalid_fill {
   using type =
-      tmpl::find<tmpl::flatten<tmpl::transform<Callbacks, get_value<tmpl::_1>>>,
-                 tt::is_a<DoubleWrapper, tmpl::_1>>;
+      tmpl::filter<tmpl::transform<Callbacks, get_fill_value<tmpl::_1>>,
+                   tt::is_a<DoubleWrapper, tmpl::_1>>;
 };
 
 template <typename InterpolationTargetTag, typename TemporalId, typename DbTags>
@@ -206,6 +196,9 @@ void fill_invalid_points(const gsl::not_null<db::DataBox<DbTags>*> box,
           },
           box);
     }
+  } else {
+    (void)box;
+    (void)temporal_id;
   }
 }
 
diff --git a/src/ParallelAlgorithms/Interpolation/Protocols/InterpolationTargetTag.hpp b/src/ParallelAlgorithms/Interpolation/Protocols/InterpolationTargetTag.hpp
index 86229466b7a7e..99bdc476586c5 100644
--- a/src/ParallelAlgorithms/Interpolation/Protocols/InterpolationTargetTag.hpp
+++ b/src/ParallelAlgorithms/Interpolation/Protocols/InterpolationTargetTag.hpp
@@ -65,7 +65,7 @@ constexpr bool if_alias_exists_assert_conforms_to_v =
  *   every element of that list conforms to the
  *   intrp::protocols::PostInterpolationCallback protocol. Only one callback
  *   with the signature with `gsl::not_null` for both the DataBox and
- *   GlobalCache (see `intrp::protocols::PostInterpolationCallback) is allowed
+ *   GlobalCache (see `intrp::protocols::PostInterpolationCallback`) is allowed
  *   in this list. Furthermore, if a callback with this signature is in the
  *   list, it must also be the *only* callback in the list. After the
  *   interpolation is complete, call this struct's `apply` function.
diff --git a/tests/Unit/ParallelAlgorithms/Interpolation/Test_InterpolationTargetVarsFromElement.cpp b/tests/Unit/ParallelAlgorithms/Interpolation/Test_InterpolationTargetVarsFromElement.cpp
index 1220c56f4acea..6071f4721dfc2 100644
--- a/tests/Unit/ParallelAlgorithms/Interpolation/Test_InterpolationTargetVarsFromElement.cpp
+++ b/tests/Unit/ParallelAlgorithms/Interpolation/Test_InterpolationTargetVarsFromElement.cpp
@@ -117,6 +117,7 @@ struct MockComputeTargetPoints
   }
 };
 
+// NOLINTNEXTLINE(cppcoreguidelines-avoid-non-const-global-variables)
 size_t num_callback_calls = 0;
 
 struct MockPostInterpolationCallback