BUG: groupby().any() returns true for groups with timedelta all NaT

pandas/core/groupby/ops.py

@@ -371,6 +371,10 @@ def _call_cython_op(
 
         is_datetimelike = dtype.kind in "mM"
 
+        if self.how in ["any", "all"]:
+            if mask is None:
+                mask = isna(values)
+
         if is_datetimelike:
             values = values.view("int64")
             is_numeric = True
@@ -380,12 +384,10 @@ def _call_cython_op(
             values = values.astype(np.float32)
 
         if self.how in ["any", "all"]:
-            if mask is None:
-                mask = isna(values)
             if dtype == object:
                 if kwargs["skipna"]:
                     # GH#37501: don't raise on pd.NA when skipna=True
-                    if mask.any():
+                    if mask is not None and mask.any():
                         # mask on original values computed separately
                         values = values.copy()
                         values[mask] = True

pandas/tests/groupby/test_grouping.py

@@ -1180,3 +1180,18 @@ def test_grouping_by_key_is_in_axis():
     result = gb.sum()
     expected = DataFrame({"a": [1, 2], "b": [1, 2], "c": [7, 5]})
     tm.assert_frame_equal(result, expected)
+
+
+def test_groupby_any_with_timedelta():
+    # Create a DataFrame with a single column containing a Timedelta and NaT
+    df = DataFrame({"value": [pd.Timedelta(1), pd.NaT]})
+
+    # Perform groupby().any() operation
+    result = df.groupby(np.array([0, 1], dtype=np.int64))["value"].any()
+
+    # Expected result: group with NaT should return False
+    expected = Series({0: True, 1: False}, name="value", dtype=bool)
+    expected.index = expected.index.astype(np.int64)
+
+    # Check if the result matches the expected output
+    tm.assert_series_equal(result, expected)