This TLS issue is based on the FACT that old versions of HP-Sync are using OLD JAVA.
Starting wtih HPE-sync 12.53 SP2, they have upgraded JAVA so TLS will not be an issue.
I recommend an upgrade of HP-sync to the latest HPE-Sync 12.55, as it will have the newer JAVA AND will be compatible with your OLD ALM 12.50 load (actually can work wtih QC11 - 12.55).
When you upgrade, PLEASE follow any special directions from any 3rd party adapters you have as they might conflict with the standard HP-Sync load - order of install events might be critical.
It is possible to have the HP-sync installer upgrade your link-data, but it is a good idea to make individual link backups (from link menu) first - just in case.