What's the risk of contracting HIV from a half or quarter syringe of filler?

The practice of using any filler other than your own syringe and almost 100% of the time used at a single injection setting is highly unusual.  I would really question your choice of injectors. 

Saving "your"  previously used syringe could open the process to very human mistakes if stored with 100's of other patient syringes,i.e.,misreading, similar names, loss of label,etc. Filling a new syringe from a master source syringe that has never been used to inject anyone is safe.

Some of the dermal fillers come in 0.5cc syringes that can be used for touch ups. Unfortunately, these are not half the price. Once a syringe is open, it should not be reused. There really is no cheap way to safely do fillers. There is alway some natural asymmetry so it is unrealistic to expect result to always be perfectly even. If it is not obvious, my first advice is to just leave it alone. If you and the doctor really feel you need more filler, maybe the doctor can work with you on the price of the additional syringe, but don't take chances. it's just not worth it!