View Items moved from S3 to Glacier via lifecycle
I am concerned you are seeing double billing. When the object is transitioned, it's moved and billed according to Glacier storage pricing. Each service charges based on average storage for the month. There is some metadata left in S3 for the transitioned object. So, if you transitioned lots of small objects, that could be the issue for the higher-than-expected billing.
For each object transitioned, 8K of metadata storage is reserved in S3. For each archived object in Glacier, Glacier adds 32K of storage for metadata. So, a worse case scenario of say 10,000 8K files transitioned would result in: S3 Charges of 8K (metadata for each file) * 10,000 (files) and Glacier charges of (8K (for each file) + 32K (Glacier metadata per file)) * 10,000.
You can read more about these AWS inner-workings here: https://docs.aws.amazon.com/AmazonS3/latest/dev/lifecycle-transition-general-considerations.html
You can see the inventory of data from the S3 bucket - as that is where inventory is managed. From the AWS Console, you should be able to see the Storage Class column when viewing files and any in Glacier should say "Glacier". You can also click on a file and then click Properties - Storage Class to see and / or change the Storage Class of an object.