Monica,

Sounds like you guys have taken the necessary steps to clean up the website and prevent it from occurring again. 404 spam links are a pain, that can often take some time to be removed from google's index all-together.

• A way to speed up the process is by changing the 404 status of these pages, and having it return a "410" error instead. This tells google it is a permanent non-existent page, and thus it will fall out of the index more quickly than a regular 404.
• In the meantime, if the number of 404 errors aren't overwhelming, you could try the "remove urls" tool within search console for these pages, which will temporarily remove them from the index all together. (emphasis on temporary)
• Marking them as fixed wouldn't be helpful, as the errors still exist, and would return to your search console not long after. (it certainly wouldn't harm your SEO, it just wouldn't be very helpful in this specific instance).

Hope that helps.

Monica,

Sounds like you guys have taken the necessary steps to clean up the website and prevent it from occurring again. 404 spam links are a pain, that can often take some time to be removed from google's index all-together.

• A way to speed up the process is by changing the 404 status of these pages, and having it return a "410" error instead. This tells google it is a permanent non-existent page, and thus it will fall out of the index more quickly than a regular 404.
• In the meantime, if the number of 404 errors aren't overwhelming, you could try the "remove urls" tool within search console for these pages, which will temporarily remove them from the index all together. (emphasis on temporary)
• Marking them as fixed wouldn't be helpful, as the errors still exist, and would return to your search console not long after. (it certainly wouldn't harm your SEO, it just wouldn't be very helpful in this specific instance).

Hope that helps.