Heroku Connect uses Salesforce's Bulk API as part of normal synchronization operation. When we know we're done with a job, we attempt to close it but can not retry indefinitely. As a result, some bulk jobs may remain open even though no batches are being added to them and they are not actively processing data.
This is not alarming or cause for concern. Bulk jobs that are open do not consume resources in Salesforce just because they are open.
The open job(s) will disappear from your Salesforce organization's Bulk Data Load Jobs dashboard 7 days after they are created. It's safer, for the health of synchronization, to ignore any open bulk jobs created by Heroku Connect.