You don't need cleaning. You need sharpening. But not a/warpsharp. (you'll lose too much detail/texture)
And, as you found out, there is no need to re-encode either

Although I would do it a bit different by upscaling the mkv's on-the-fly in MPC as follows:
- Load mkv with Media Player Classic >> Play >> Filters >> ffdshow Video Decoder >> Properties
- Checkmark Resize & Aspect >> Specify H & V Size: 1280x720 (maybe select Resize to screen resolution if your computer can handle it)
- Checkmark Sharpen >> Unsharp Mask >> Set to ~80 is pretty good for School Rumble IMO (other sources will be different)
- Checkmark Deband >> Use defaults
(Note: you may need to move these three filters up/down as needed so they are in that particular sequential order)
One really nice thing about this method is any [soft] subtitles will
literally be HD.
(It's not just an upscale trick like with the video; the subs are
actually rendered at whatever resolution you choose... so you'll have gorgeous subs, even if the video doesn't upscale that nicely)
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Generally I wouldn't mess with colors-- I find it usually creates more problems than any gain you think you are seeing (unless you are doing color correction scene-by-scene).
Levels might be a different matter though, so it may be worth noting that the original DVDs will usually look more dull since they have a clamped TV luma range (16-235; blacks won't really be black; whites won't really be white), so you would want to expand to PC range (00-255?)... but anyways color correction is a whole different beast...
As for using the 'AviSynth Filter,' you first need to make sure avisynth and any associated plugins are actually installed on your computer. Be sure to check add ffdshow video source. Then type any filter commands you like into the dialogue box (but don't include your sourcecall-- just the filter commands). Checking buffer ahead/back 10 10 can really improve performance (especially if you want to do things like frame-interpolation on-the-fly for live action). Although you probably won't need avisynth in this case, unless you wanted to do a true remaster; but then you would want to re-encoding the whole thing, and I don't think you really want to do that... and even then... you would have to know what commands to use and when it's appropriate to use them... so ffdshow filters are more convenient for your purposes.
But if you wanted to take that route, here's a dirty summary of the guide everyone is referring to

:
viewtopic.php?f=45&t=103579#p1373940As you have probably suspected by now, some DVD's don't look that great to begin with. Welcome to DVD quality

That's just how it is.
However, they do have the
potential to look the best since you are starting with the original detail (...or as much detail as possible anyway...)
Also, I just have to point out: that DBGT remaster example is devoid of all fine detail/texture. It looks like watching the Flintstones.
Way over-filtered.