diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index fc55e1c530272..13c4c0161aeee 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -494,7 +494,7 @@ def delete(self, loc):
         """
         new_tds = np.delete(self.asi8, loc)
 
-        freq = "infer"
+        freq = None
         if is_integer(loc):
             if loc in (0, -len(self), -1, len(self) - 1):
                 freq = self.freq
@@ -505,7 +505,7 @@ def delete(self, loc):
                 if loc.start in (0, None) or loc.stop in (len(self), None):
                     freq = self.freq
 
-        return TimedeltaIndex(new_tds, name=self.name, freq=freq)
+        return self._shallow_copy(new_tds, freq=freq)
 
 
 TimedeltaIndex._add_comparison_ops()
diff --git a/pandas/tests/indexes/timedeltas/test_timedelta.py b/pandas/tests/indexes/timedeltas/test_timedelta.py
index 7703fbbbcad2a..3b52b93fa6369 100644
--- a/pandas/tests/indexes/timedeltas/test_timedelta.py
+++ b/pandas/tests/indexes/timedeltas/test_timedelta.py
@@ -201,6 +201,13 @@ def test_append_numpy_bug_1681(self):
         result = a.append(c)
         assert (result["B"] == td).all()
 
+    def test_delete_doesnt_infer_freq(self):
+        # GH#30655 behavior matches DatetimeIndex
+
+        tdi = pd.TimedeltaIndex(["1 Day", "2 Days", None, "3 Days", "4 Days"])
+        result = tdi.delete(2)
+        assert result.freq is None
+
     def test_fields(self):
         rng = timedelta_range("1 days, 10:11:12.100123456", periods=2, freq="s")
         tm.assert_index_equal(rng.days, Index([1, 1], dtype="int64"))