To reproduce:

• summon two invisible cows using command below
• leash them both to a fence
• observe extra leads rendering between these cows and possibly other entities around

There are no issues when entities are visible.

Commands used:

/summon cow ~ ~ ~
/summon cow ~ ~ ~ {ActiveEffects:[{Id:14,Amplifier:100,Duration:999999}]}
/give saharNooby lead

Leashed invisible entities are used in Minecraft to create hanging wires.