Add an action to Moderator Logs?
 

So long story short, we have a mod that allows moderators to click a red tick which is below each post, which clicked, turns the tick green to effectively tell other moderators that this post has been checked (ticking post #23 for example.. also marks all previous posts in that thread as marked too, with a green tick) so if there are 50 posts in a thread. Ticking the last post essentially marks the whole thread with a green tick.

How do we go about adding said action to the moderators log?
So that it'll display in the logs when said users have clicked the red tick?

Anyone know how?

Your best option is to have whom ever made your modification to add this functionality. If they are no longer available you will need to hire a developer who has a good underlying understanding of vBulletin and its coding. Unfortunately finding a good VB 4 developer is becoming increasingly difficult.