I have some survey data and a sketch of the cave passage on TopoDroid. I can choose to hide legs, stations and splay shots to just view the sketch. When I export it as png though, everything is included and the picture becomes messy. What is the simplest and quickest way of exporting just a sketch (either as png or svg or even as jpg)?

I've had mixed luck at exporting pngs from topodroid. Either way I would email Marco directly as I believe it needs improving...

I've not had much luck with TopoDroid sketches either.
The Therion TH2 export doesn't suit me because all the walls get converted to Therion lines with so many points it is very hard to edit them. They are rarely in the right place as the drawing accuracy on an Android phone is rubbish.
The PNG isn't much use as a background as it doesn't have the stations, so scraps can't be located.

What I do is export an XVI file and use that as the background in the TH2 file. I open the PNG in a separate window and use it as a reference for adding in the bits I sketched.
It's not ideal, but it works...

If you turn on advanced mode you can change the detail of the png files. But png files can only be a certain length due to file format issues. So 1000 feet of passage won't work in a png file.

The way that I export is to is a .th and .th2 file. I then load these in therion, fix any issues with compile, and export to an svg file. Topodroid seems to work 95% of the time straight in therion. It seems to struggle with "user" lines and you have to add the options to "slope" lines.

I then take my svg file and make it a background layer in either inkscape or illustrator. Then I re-draw the final map in those programs just like I would redraw a sketch that was on paper. Not my favorite workflow. I'd be happy if someone comes up with something better.