The Gantt components supports link context menu. It can be activated by right-clicking the link.
JavaScript
Use .contextMenuLink property:
dp.contextMenuLink = new DayPilot.Menu({items: [
{text:"Show link ID", onclick: function() { alert("Link ID: " + this.source.data.id);} },
{text:"Delete link", onclick: function() { dp.links.remove(this.source);} }
]});