Strange noise on DDS
Your phantom signals are digital measurement errors from undersampling and a low alias frequency is the result.


Comments


Your analog scope shows significant DC , low frequency components, which you may want to  reject with a HPF.
The filter design must be driven from a current source to work as designed with 6dB loss in the passband, since impedance ratio is 1/2.  If this is my false assumption,then R1 should be in series with a voltage source.
The values shown are for 80MHz LPF may has 2dB ripple in response in pass band but stopband begins at 100MHz, @ -66 dB.  If you don't want the ripple,  use, Chebyshev Type 2. The steep skirt as a large ripple penalty in your Cauer design or change the ripple factor.


Suggestion.  Learn how to match or isolate output and load impedance  so that your test measurement impedance does not introduce a false circuit load.  e.g.  dont load filter with a 20pF probe. Use 150 + 50 Ohm scope or Spectrum Analyzer or use a 1pF FET probe.