Two-way integration with other products

[ServiceDesk Plus]

ME ServiceDesk Plus is an ITSM tool. We currently user Jira API to move a ticket from our application to Jira. Some of our customers use Jira in unison with our product. They would like two-way integration.

As of now, we are using Jira API to create a issue w/o any problems. For two way integration, when an issue/bug is updated in Jira, we would like to update in our product as well.

We considered webhooks in post function, but webhooks only seem to support POST calls and not PUT calls as we require for our product  Also looked into email notifications, but we are unable to edit the content of the email that goes out of Jira.

How do we go about this? Any help would be appreciated.