Many people say Glycerin is not kosher in mouthwash. Just fyi.
MouthwashRav Schwartz holds mouthwash doesn't require hashgachah, but it is preferred to use a kosher variety if available
From the CRC OTC Medicine Listhttp://www.crcweb.org/OTCMedicineReport.pdf
Star-K has all Scope Mouthwash on the recommended personal care list for Pesachhttps://www.star-k.org/articles/wp-content/uploads/QuickPickPersonalCare_2019.pdf