Sallie, ready to go for the crux which is up and l...
This route is found on the right side of the first clean face just right of the water falls. Moderate climbing to reach first bolt. Gear can be placed above this in cracks as the second bolt is quite a ways away. Above the second bolt on the left is another bolt which could be used although it's a bit tough to get to. The climb doesn't go out here as this bolt is used on a variation of the climb to the left but it does help as protection. Although the climbing eases off to 5.8, there is a long runout to the last bolt but trad gear can be placed in the crack to the right and/or a hole on the left. The last moves over the top are a surprise.
Tresa Black's Rock Climbing the San Francisco Bay Area guide book rates this as 5.10c. As described here there is nothing harder than 5.9+, if that. The only way I can see to make this harder is to climb the thin face on the bottom just left of obvious path to the first bolt. This doesn't make sense but is fun to do.
Three bolts to two bolt anchor. Trad gear can be placed in two sections to lesson the runouts between bolts. A large hex makes for a bomber placement lower down and a medium large cam fits nicely in a hole higher up.
The 10c way is not shown in the Falcon Guide by Tresa Black. After the second bolt of the Greebo, traverse up and left to a third bolt via a series of mantles (5.10c). After you clip the third bolt you can do the same 5.11a variation as the Oracle (thin, thin face). See Rock Climber's Guide to Skyline Boulevard (2000), p. 81, to corroborate.