diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index cd1cb0b64f74a..e8fdaf0ae5d49 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -462,6 +462,7 @@ Datetimelike
 - Bug in :meth:`DatetimeIndex.to_period` not infering the frequency when called with no arguments (:issue:`33358`)
 - Bug in :meth:`DatetimeIndex.tz_localize` incorrectly retaining ``freq`` in some cases where the original freq is no longer valid (:issue:`30511`)
 - Bug in :meth:`DatetimeIndex.intersection` losing ``freq`` and timezone in some cases (:issue:`33604`)
+- Bug in :class:`DatetimeIndex` addition and subtraction with some types of :class:`DateOffset` objects incorrectly retaining an invalid ``freq`` attribute (:issue:`33779`)
 
 Timedelta
 ^^^^^^^^^
diff --git a/pandas/tests/tseries/offsets/test_yqm_offsets.py b/pandas/tests/tseries/offsets/test_yqm_offsets.py
index 79a0e0f2c25eb..13cab9be46d37 100644
--- a/pandas/tests/tseries/offsets/test_yqm_offsets.py
+++ b/pandas/tests/tseries/offsets/test_yqm_offsets.py
@@ -64,6 +64,7 @@ def test_apply_index(cls, n):
     ser = pd.Series(rng)
 
     res = rng + offset
+    assert res.freq is None  # not retained
     res_v2 = offset.apply_index(rng)
     assert (res == res_v2).all()
     assert res[0] == rng[0] + offset
diff --git a/pandas/tseries/offsets.py b/pandas/tseries/offsets.py
index 8ba10f56f163c..b419d5ccc10b4 100644
--- a/pandas/tseries/offsets.py
+++ b/pandas/tseries/offsets.py
@@ -1147,9 +1147,7 @@ def apply(self, other):
     @apply_index_wraps
     def apply_index(self, i):
         shifted = liboffsets.shift_months(i.asi8, self.n, self._day_opt)
-        # TODO: going through __new__ raises on call to _validate_frequency;
-        #  are we passing incorrect freq?
-        return type(i)._simple_new(shifted, freq=i.freq, dtype=i.dtype)
+        return type(i)._simple_new(shifted, dtype=i.dtype)
 
 
 class MonthEnd(MonthOffset):
@@ -1868,11 +1866,7 @@ def apply_index(self, dtindex):
         shifted = liboffsets.shift_quarters(
             dtindex.asi8, self.n, self.startingMonth, self._day_opt
         )
-        # TODO: going through __new__ raises on call to _validate_frequency;
-        #  are we passing incorrect freq?
-        return type(dtindex)._simple_new(
-            shifted, freq=dtindex.freq, dtype=dtindex.dtype
-        )
+        return type(dtindex)._simple_new(shifted, dtype=dtindex.dtype)
 
 
 class BQuarterEnd(QuarterOffset):
@@ -1954,11 +1948,7 @@ def apply_index(self, dtindex):
         shifted = liboffsets.shift_quarters(
             dtindex.asi8, self.n, self.month, self._day_opt, modby=12
         )
-        # TODO: going through __new__ raises on call to _validate_frequency;
-        #  are we passing incorrect freq?
-        return type(dtindex)._simple_new(
-            shifted, freq=dtindex.freq, dtype=dtindex.dtype
-        )
+        return type(dtindex)._simple_new(shifted, dtype=dtindex.dtype)
 
     def is_on_offset(self, dt: datetime) -> bool:
         if self.normalize and not _is_normalized(dt):