She lent the Black March to Baam in the 1st Floor, which is kinda completely isolated from the other floors, since Regulars start to climb the Tower from the second floor. And the more you climb the Tower the more eyes you will have on you. Especially, when you climb the Tower with a member of the 10 Great Families or a Zahard Princess. Additionally, it doesn't look like it's easy to keep a 13 Month Series a secret from others, especially when you start using its ignited form in "public". The 13 Month Series resonate when in close proximity. Rak could even feel that the Black March was special without even witnessing its ignited form. I expect every formal Princess to recognize a 13 Month Series upon seeing them. The problem is not for Yuri to hide the fact that she gave away her 13 Month Series. The biggest issue here is for Baam/Androssi to use a 13 Month Series without others recognizing it as such.
I personally liked the interaction between Baam and the Black March a lot. But SIU basically made it impossible for him to possess it in the long run.