BUG : Add Deprecation FutureWarning for parse function call

doc/source/whatsnew/v2.0.0.rst

@@ -1304,6 +1304,7 @@ I/O
 - Bug in :meth:`DataFrame.to_dict` not converting ``NA`` to ``None`` (:issue:`50795`)
 - Bug in :meth:`DataFrame.to_json` where it would segfault when failing to encode a string (:issue:`50307`)
 - Bug in :func:`read_xml` where file-like objects failed when iterparse is used (:issue:`50641`)
+- Bug in :func:`read_excel` where passing invalid argument name ``headers`` to :meth:`parse` doesn't raise error (:issue:`50953`)
 
 Period
 ^^^^^^

pandas/io/excel/_base.py

@@ -21,6 +21,7 @@
     cast,
     overload,
 )
+import warnings
 import zipfile
 
 from pandas._config import (
@@ -47,6 +48,7 @@
     Appender,
     doc,
 )
+from pandas.util._exceptions import find_stack_level
 
 from pandas.core.dtypes.common import (
     is_bool,
@@ -1553,11 +1555,49 @@ def parse(
         Equivalent to read_excel(ExcelFile, ...)  See the read_excel
         docstring for more info on accepted parameters.
 
+        .. deprecated:: 2.0.0
+            Arguments other than sheet_name by position may not work.
+
         Returns
         -------
         DataFrame or dict of DataFrames
             DataFrame from the passed in Excel file.
         """
+        arguments = list(kwds.keys())
+        allowed_kwargs = [
+            "sheet_name",
+            "header",
+            "names",
+            "index_col",
+            "usecols",
+            "squeeze",
+            "dtype",
+            "engine",
+            "converters",
+            "true_values",
+            "false_values",
+            "skiprows",
+            "nrows",
+            "na_values",
+            "keep_default_na",
+            "na_filter",
+            "verbose",
+            "parse_dates",
+            "date_parser",
+            "thousands",
+            "decimal",
+            "comment",
+            "skipfooter",
+            "convert_float",
+        ]
+        # Check for any invalid  kwargs
+        if [argument for argument in arguments if argument not in allowed_kwargs]:
+            warnings.warn(
+                f"{type(self).__name__}.parse is deprecated. "
+                "Arguments other than sheet_name by position may not work.",
+                FutureWarning,
+                stacklevel=find_stack_level(),
+            )
         return self._reader.parse(
             sheet_name=sheet_name,
             header=header,

pandas/tests/io/excel/test_readers.py

@@ -1684,3 +1684,11 @@ def test_corrupt_files_closed(self, engine, read_ext):
                     pd.ExcelFile(file, engine=engine)
                 except errors:
                     pass
+
+    def test_read_excel_parse_warning(self, read_ext):
+        # GH50953
+        msg = "Arguments other than sheet_name by position may not work."
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            with pd.ExcelFile("test1" + read_ext) as excel:
+                excel.parse("Sheet1", headers=[0, 1, 2])
+                # invalid argument 'headers' should give warning for deprecation