Ignore 'action' querystring parameter
I think we need more information to be able to consider possible solutions. I personally wouldn't do anything in Craft, rewriting this URL before it hits the application would be cleaner. I don't know if it's possible to configure the 'action' parameter name in Craft so let's assume not.
Are the referring URLs always the same? In other words, is the visitor always returned to the same URL on your site (which contains &amp;action=something)? If so, a fairly simple Apache/nginx rewrite URL could be written to remove the parameter from the request.
If not, it may still be achievable with a rewrite rule if you're willing to trust the HTTP_REFERER variable.