Since JRiver processes all sound at 64-bits, when changing back to 24-bit or 32-bit for output you need to use dither. Dither should always be turned on unless you are using a VST plugin for dither and are comfortable configuring it.
"24 bit in a 32 bit package" - When using an ASIO driver, many DAC's will request that JRiver deliver the audio as 32-bits. You can see this by looking at the Audio Path. However, even though the DAC's request 32-bits, the DAC is still has 24-bit output. This means the DAC will truncate the last 12 bits. To properly dither and not make things worse, you need to set check "24-bit in a 32-bit package." You really can check it for any 24-bit DAC. Some pro audio users might have a mixer that is part of their ASIO driver. They might want to get the 32-bit output from JRiver since they are controlling the dither with their ASIO drivers and mixer. Their mixer is also processing data at 32-bits or higher. In this case they would leave the option unchecked.
Note: Dither is only used when any processing is done. If you don't do any processing including volume control, then there is no dither. So, you really can leave it turned on all the time and for most people they should check "24-bit in a 32-bit package."