Restrict the acceptable artifact tags to all existing uploadable combinations
diff --git a/tools/run_tests/artifacts/build_artifact_python.sh b/tools/run_tests/artifacts/build_artifact_python.sh
index a708f2e..91eb21f 100755
--- a/tools/run_tests/artifacts/build_artifact_python.sh
+++ b/tools/run_tests/artifacts/build_artifact_python.sh
@@ -79,12 +79,12 @@
 if [ "$GRPC_BUILD_MANYLINUX_WHEEL" != "" ]
 then
   for wheel in dist/*.whl; do
-    "${AUDITWHEEL}" show "$wheel" | tee /dev/stderr | grep \"manylinux
+    "${AUDITWHEEL}" show "$wheel" | tee /dev/stderr |  grep -E -w 'manylinux(1|2010)_(x86_64|i686)'
     "${AUDITWHEEL}" repair "$wheel" -w "$ARTIFACT_DIR"
     rm "$wheel"
   done
   for wheel in tools/distrib/python/grpcio_tools/dist/*.whl; do
-    "${AUDITWHEEL}" show "$wheel" | tee /dev/stderr | grep \"manylinux
+    "${AUDITWHEEL}" show "$wheel" | tee /dev/stderr |  grep -E -w 'manylinux(1|2010)_(x86_64|i686)'
     "${AUDITWHEEL}" repair "$wheel" -w "$ARTIFACT_DIR"
     rm "$wheel"
   done