I have only been using Jira OnDemand so I am not sure if this applies to self hosted versions as well. The problem is that no webhook events are being fired when adding or removing remote links on issues.

Other kind of activities like adding comments or labels to issues trigger events properly.

I don't know if this is related to the problem or not, but even searching by updated date doesn't work properly when it comes to remote link actions. If you add or remove a remote link to an issue, this is immediately reflected in the value displayed for Updated, under Dates section, in the issue details screen. If you then search for issues that were modified in an interval that includes that date, the issue which had the remote link added or removed will not be displayed (unless, there have been other updates as well in the interval).