What the Clown Master did was, take out the Clown Zero and hand it over to Shiro. It was up to him to use it however he wanted. It was now his property and was the reward for clearing the dungeon.
He didn't give Shiro any sort of special storage item to store the puppet. He just wanted Shiro to carry it out. But it was by no means causing any inconvenience to Shiro.
He had an inventory after all so he could easily store the puppet inside it which he actually did and surprised the Clown Master.
"Ahem, so…"
The clown master pretended to not be surprised and continued to talk.
"Since you have cleared the dungeon, I would like if you would come with me to visit the Earth God."
Hearing this directly from the Clown Master was weird, but Shiro had no reason to refuse. It was exactly what he wanted to happen. But before he could go, he wondered where Tonnis could have gone.
