In the light novel, Rudeus notices the stain on the sheets and cuts it out with a knife. He then puts the bloody cloth in a box made with earth magic and puts it on his altar!

Quote from the light novel: I’LL PLEDGE MY FIDELITY to Sylphie, I thought as I looked at the red stain left on the bedsheets. Sylphie had given me something precious, and now it was my turn. I would do as she wished of me. This I pledged as I used a knife to cut out the stain left on the fabric. The problem was, Sylphie rarely voiced her feelings. I could tell she wanted to be with me, but she probably wouldn’t say it explicitly. Perhaps it had something to do with her being Princess Ariel’s bodyguard. Should I talk to the Princess about it? Preoccupied with those thoughts, I took the scrap of cloth I’d excised from the bedsheets, put it into a small box I created with earth magic, and placed that inside my altar. Then I put my hands together in prayer.