LOG.debug seems reasonable level for it.
I disagree, without the "Starting a new period" message it's very difficult to diagnose the block pool scanner in production scenarios. Production cannot run with debug enabled due to other cases where debug logging is actually expensive. So making this critical status message a LOG.debug makes it effectively useless.
I'd be OK with replacing all of these logs with a useful set of (for example) JMX metrics so that the scanner is more observable in an automatable/graphable fashion, but until that happens, this message needs to stay in at LOG.info.