Can an oscilloscope add a frequency component to my signal?
Those sidelobes are the result of the limited resolution of the data from the DSO, along with the fact that the sampling in the DSO is not precisely synchronized to the DDS output waveform, which results in a tiny amount of apparent (not actual) amplitude modulation of the actual waveform.

If you oversample and apply a proper sin(x)/x reconstruction filter to your DSO data, those sidelobes will disappear.