LTM member in pool has status offline (disabled by parent)

Administratively disabled means that someone disabled the node on the F5 directly (on the GUI / CLI / programmatically).

When looking at the pool member in the F5 configuration utility (GUI):

• The diamond shape indicates that its health check is failing
• The grey colour indicates that it was disabled by parent (i.e. at a node level)

The reason why you are seeing a grey diamond symbol as opposed to a black diamond symbol is due to the fact that it was disabled at a node (parent) level.

If it was disabled at a pool member level, then you would have seen a black diamond symbol instead.