At my work place, we use an external client's web application monitor and respond to support tickets of our clients. the problem with that application is that it does not house a field to enter the actual effort (hours worked on a particular ticket) to be stored in the database.

What is needed to write a plug-in for Internet Explorer that would get triggered on a button click on a certain webpage and save some data in an external database?

That is, if the support personnel is closing the ticket after resolving it, is it possible to invoke that plugin that asks the personnel to enter the effort spent on that ticket and store it in an external database?

We can't modify the web application as it is vendor supplied and not an in-house product.