The Linksys ATA Administrator Guide is short on specifics:

The minimum jitter buffer size is 30 milliseconds or (10 milliseconds + current RTP frame size), whichever is larger, for all jitter level settings. However, the starting jitter buffer size value is larger for higher jitter levels. This setting controls the rate at which the jitter buffer size is adjusted to reach the minimum. Select the appropriate setting: low, medium, high, very high, or extremely high. The default is high.

Set up a LAN call between the ATA and another SIP device (or even the other port on the ATA). Test with corded analog phones. Put your computer mic next to the earpiece of the receiving phone and start recording. Bang on the mic of the sending phone. Open the recording in an audio editor and measure the time difference between the sent and received bangs. Subtract 20 ms for packetization and ~5 ms for processing delay and that's your jitter buffer. Test at the start of a call and after e.g. 10, 30, 60, and 120 seconds, which should show you the adjustment rate.