How Best to Handle Inherited 404s on Purchased Domain

[russell_ms]

We purchased a domain from another company and migrated our site over to it very successfully. However, we have one artifact of the original domain in that there was a page that was exploited by other sites on the web. This page allowed you to pass any URL to it and redirect to that URL (e.g. http://example.com/go/to/offsite_link.asp?GoURL=http://badactor.com/explicit_content).

This page does not exist on our site so the results always go to a 404 on our site. However, we find that crawlers are still attempting to access these invalid pages.

We have disavowed as many of the explicit sites as we can, but still some crawlers come looking for those links. We are considering blocking the redirect page in our robots.txt but we are concerned that the links will remain indexed but uncrawlable.

What's the best way to pull these pages from search engines and never have them crawled again?

UPDATE: Clarifying that what we're trying to do it get search engines to just never try to get to these pages. We feel the fact they're even wasting their time on getting a 404 is what we're trying to avoid. Is there any reason we shouldn't just block these in our robots.txt?

[Rajesh.Prajapati]

You need to do one thing with those 404 pages. Move them as 410 status code. Redirection is not good practice for the same.

[pilesofpillows]

I would actually recommend redirecting it to the homepage. If you have a Wordpress website and a bunch of 404 pages, you can install a free plugin called "All 404 to Homepage" and this will solve the problem. I would, however, recommend that if you have replacement pages or pages covering similar content, that you redirect those to the corresponding replacement page.

[GastonRiera]

FOR THE LOVE OF GOD DONT REDIRECT  404s TO THE HOME!

This is terrible advice. Doing that you'll turn those 404s into soft 404s, making them more problematic than ever.

[GastonRiera]

Hi there,

I'm considering that you have over 500k URLs, to be worrying about crawl efficiency. If you have less than that, please don't worry.

Having 404s is completely fine, and google will eventually lower their crawl frequency to those pages. 
Blocking them in robots.txt will cause to google stop crawling them, but never to never remove them from the index.
My advice here: don't block them in robots.txt

As Rajesh pointed out, you could force those 404s into 410 to tell Google that they are gone forever. Yet, Google said that they treat 404s and 410s as the same.
John Mueller said over a year ago that 4xx status codes don't incur in crawl wastage. You can check it our in these Webmasters hangout notes - Deepcrawl

Hope it helps,
Best luck.
Gaston