Remove compatability badges from READMEs. (#9035)

Author: busunkim96

README.rst

@@ -1,7 +1,7 @@
 Core Library for Google Client Libraries
 ========================================
 
-|pypi| |versions| |compat_check_pypi| |compat_check_github|
+|pypi| |versions| 
 
 This library is not meant to stand-alone. Instead it defines
 common helpers used by all Google API clients. For more information, see the
@@ -12,10 +12,6 @@ common helpers used by all Google API clients. For more information, see the
 .. |versions| image:: https://img.shields.io/pypi/pyversions/google-api_core.svg
    :target: https://pypi.org/project/google-api_core/
 .. _documentation: https://googleapis.dev/python/google-api-core/latest
-.. |compat_check_pypi| image:: https://python-compatibility-tools.appspot.com/one_badge_image?package=google-api-core
-   :target: https://python-compatibility-tools.appspot.com/one_badge_target?package=google-api-core
-.. |compat_check_github| image:: https://python-compatibility-tools.appspot.com/one_badge_image?package=git%2Bgit%3A//github.com/googleapis/google-cloud-python.git%23subdirectory%3Dapi_core
-   :target: https://python-compatibility-tools.appspot.com/one_badge_target?package=git%2Bgit%3A//github.com/googleapis/google-cloud-python.git%23subdirectory%3Dapi_core
 
 
 Supported Python Versions