To “repair” an existing image, you’d want to use “healing”, “retouch”, or a clone tool. It depends on the software you’re using for the edit. Healing / retouching tries to match to surrounding areas, cloning is a simple copy and paste from one area to another, often with feathering.
For what it’s worth, I couldn’t find where this might exist in RawTherapee, either in the app itself, in the docs, or in a web search. (I know darktable and GIMP both have both features, the simple clone tool and a smart tool called “healing” or “retouch”.) Perhaps someone else could chime in on how to do this with RawTherapee. (The answer might be to edit externally, like in the GIMP.)
To “fix” new pictures you’ll snap in the future, consider using a wider aperture (a lower f/stop number). The higher the f/stop, the smaller the aperture, the more depth of field you’ll get in the image. In other words, you’ll have everything from the closest subjects (in this case, your dust flecks) all the way to the mountains. If you change the depth of field by adjusting the aperture to a smaller number, you can change what’s in focus — and move the focus to around infinity (far away from the dust on your sensor)… ideally, set it to the hyperfocal distance, which is before infinity and let the depth of field (which would include infinity) do the rest, to make everything in the photo sharp (that you want sharp).
Besides, a Micro Four Thirds camera has a diffraction limit of around f/8, so you’ll have overall image quality losses above that (like f/16 or f/32). Around these apertures you’ll see more pronounced dust spots anyway.
There are circumstances where you do want a tiny aperture (high f-stop number). It still can make sense to shoot f/16 on a MFT lens, as everything is a tradeoff. But note that when people are talking about shooting scenery with f/11, f/16, f/18, etc. — they’re usually talking about full frame or APS-C sensor sizes. It’s usually around f/5.6, f/8, f/11 (depending on the subject(s), lighting, lens, etc.) instead for MFT.
As Micro Four Thirds cameras have a smaller sensor than APS-C and “full frame”, you do get some depth of field “for free” (for either good or bad, depending on what you’re going for). For scenery, it’s great — you’ll have more in focus at once at a lower f/stop. A lot of people do shoot at f/8 on MFT for scenery. (But it all depends on lots of tradeoffs, just like the rest of photography.)
If you do want to use a high f/stop number, then you’ll basically have to clean your sensor glass (some cameras have this built in for typical amounts of dust) or post process to take care of the dust. This is just one of the downsides to digital cameras with interchangeable lenses that we all live with. Film cameras don’t have the sensor dust problem as much (as the film advances and often takes dust flecks with it). There are, thankfully, a lot of upsides to being able to swap out lenses, of course.
If you are shooting a landscape where the subject matter is far away, you can make everything simple: You could drop the f/stop number down a bit (open the aperture wider) to a sweet spot between aberrations (lens irregularities on a “wide-open” aperture setting on a lens) and diffraction (when a lens starts making everything a bit blurry) and simply focus on infinity.
TL;DR: Consider shooting at f/8 or lower on a Micro Four Thirds camera to keep your subject(s) in focus and minimize diffraction and dust spots.
(For what it’s worth, throw out all these rules of thumb when you’re doing macro. For that, you often want a deep depth of field (high f/stop number) and have to do focus stacking to get an even deeper depth of field. And long exposures are also a bit different, especially when not shooting the sky. But for most standard photos, the above applies.)