Yes the problem is present with running on batteries therefore the PSU/rectifier/transformer etc should be excluded.
There are LOT of switch mode regulators inside oscilloscope.
With battery alone used for power there is only one what is not working.
There is two sources for raw 8.4V "main" power. Battery or external 110-240V.
After this there is lot of switch mode power supplies/regulators. Also in power supply module there need also do negative (-7.5V).
Power supply unit produce only raw 8.4V and -7.5V voltages. These are not (in mainstream) used directly but they are used for sub power supplies / regulators around of oscilloscope.
Some of these switch mode circuits produce now high amount of parasitic oscillations/ringing. (Why? Perhaps some components more deep parameters... all know that inductor is example 8.8uH but there is also many other things.. core material, internal parasitic capasitances...etc.. Also perhaps layout changes may have some role.
This whole case need more deep investigation.
Good thing is: These "noises" do NOT pollute signal pathways inside oscilloscope!
My recommendation for users and specailly now before this is solved:
take special care about probing!
We know now that clean signal example via well shielded and matched coaxial and there can not see any sign of this problem.
And nearly as good situation is with oscilloscope probe IF you do not use probe GND "long wire" "inductor" for signal GND. From oscilloscope GND arrive lot of "noise" signals ant they trawel via this wire and continue they "travel" to somewhere forward... This GND wire is inductance for these high frequency components and it produce signal over this GND wire etc bad efects.
You can reduce this problem if you need look low level signals.
If it is possible do NOT use probe GND wire at all.. take it away and do probing like this attached image,
even if you handle low frequency signals. (becouse, part of this noise is high frequency and these need handle so that they do not pollute signal outside of oscilloscope using this GND wire reactance)
With slow horizontal speeds you see just spikes and random "chaos" but in real world they are high frequency "signals". It can easy see using example other fast oscilloscope and spectrum analyzer. (also what you see depends samplerate becouse with low freq signals you use low horz speed and perhaps low samplearate what affect aliasing with these high freq components of signal (these noise components)
This image is good "thumb rule" how you need probe. And keep this GND connect as short as possible (around same as center pin..)
Image is borroved here
http://www.power-eetimes.com/en/evaluating-a-dc-to-dc-converter-in-the-lab.html?cmp_id=71&news_id=222904246I have tested and example with 10mVpp 1kHz signal from enough clean signal generator and using Owon probe with 1x setting and scope 5mV/div give clean signal. With GND longwire... can see only " total chaos". (fatty trace where noise p-p is around same (10mVpp) as signal itself. )
And more fun. If probe 10x and signal 100mVpp noise is nearly also 100mVpp. Of course then what you see depends samplerate.
With short GND noise is gone.
This is NOT solution for this problem. But in many cases before real help, with this you can walk in many cases.
This just like first help before doctors come...