diff --git a/pyproject.toml b/pyproject.toml
index ddc903d6af9d7..7446af9579578 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -41,7 +41,6 @@ warn_no_return = "False"
 # the list can be generated with:
 # mypy | tr ':' ' ' |  awk '{print $1}' | sort | uniq | sed 's/\.py//g' | sed 's|\/|\.|g' | xargs -I {} echo '"{}",'
 module = [
-    "pytorch_lightning.callbacks.finetuning",
     "pytorch_lightning.callbacks.model_checkpoint",
     "pytorch_lightning.callbacks.progress.rich_progress",
     "pytorch_lightning.callbacks.quantization",
diff --git a/src/pytorch_lightning/callbacks/finetuning.py b/src/pytorch_lightning/callbacks/finetuning.py
index 4a7067f56c697..ad45ff8b0591b 100644
--- a/src/pytorch_lightning/callbacks/finetuning.py
+++ b/src/pytorch_lightning/callbacks/finetuning.py
@@ -32,8 +32,8 @@
 log = logging.getLogger(__name__)
 
 
-def multiplicative(epoch):
-    return 2
+def multiplicative(epoch: int) -> float:
+    return 2.0
 
 
 class BaseFinetuning(Callback):
@@ -79,7 +79,7 @@ class BaseFinetuning(Callback):
         ...             )
     """
 
-    def __init__(self):
+    def __init__(self) -> None:
         self._internal_optimizer_metadata: Dict[int, List[Dict[str, Any]]] = {}
         self._restarting = False
 
@@ -94,7 +94,7 @@ def load_state_dict(self, state_dict: Dict[str, Any]) -> None:
             self._internal_optimizer_metadata = state_dict["internal_optimizer_metadata"]
         else:
             # compatibility to load from old checkpoints before PR #11887
-            self._internal_optimizer_metadata = state_dict
+            self._internal_optimizer_metadata = state_dict  # type: ignore[assignment]
 
     def on_fit_start(self, trainer: "pl.Trainer", pl_module: "pl.LightningModule") -> None:
         # restore the param_groups created during the previous training.
@@ -122,10 +122,11 @@ def flatten_modules(modules: Union[Module, Iterable[Union[Module, Iterable]]]) -
             modules = modules.values()
 
         if isinstance(modules, Iterable):
-            _modules = []
+            _flatten_modules = []
             for m in modules:
-                _modules.extend(BaseFinetuning.flatten_modules(m))
+                _flatten_modules.extend(BaseFinetuning.flatten_modules(m))
 
+            _modules = iter(_flatten_modules)
         else:
             _modules = modules.modules()