According to Wikipedia the Terminologia Anatomica (international anatomy standard) the lymphatic trunks are part of the cardiovascular system instead of the lymphoid system.
Why did they make that choice?
The definition of "vascular" is as follows:-
By this defninition, the cardio-vascular system doesn't need to include only the blood vessels and the heart. It includes all conducting and distributing vessel elements including those which carry the lymph-Lymphatic vessels. The cardiovascular system stands for the "circulatory system"+ the heart tissues and since lymph is an essential part of the circulation (of nutrients, hormones, wastes etc), the cardiovascular system must include the lymphatic system.
Lymphoid system is a completely different entity which includes spleen, the lymphoid tissue (MALT), the lymph nodes and the lymph vessels. Hence the lymphatic vessels belong to both, the cardiovascular system and the lymphatic system, but the MALT and Spleen (arguable and disputed) are only a part of the lymphatic system and not of the cardiovascular system.
MALT= Mucosal Associated Lymphoid TIssue