I purchased this nice whole-leaf oolong tea this afternoon.   I steeped it in 200 F water for 3 minutes (as directed) in my tea steeping basket:   And when I pulled out the basket, there were some uninvited guests remaining:   Did I do something wrong? I thought this was the kind of results to expect from tea "dust" that might be expected in a bag, but this is whole-leaf tea. Do I need to pre-sift my tea, or something? I'm afraid that as these remnant sit in the tea, they will make it bitter. 
In Chinese tea "rituals" they "rinse" the leaves with hot water before steeping. Fill the pot with water and dump it out right away. Then fill your pot and continue as normal. This gets rid of the majority of the "dust". Like the others said, yes it's normal.  