Snapping to sketch' geometry is now available in development version and soon in 3.14, thanks to this PR. Here's how to do it:
Create a permanent vector layer.
Add polygon feature
Snapping toolbar > Self-Snapping
In QGIS 3.4 (and probably before that), you can use the ‘Vertex’ tool (which is next to ‘Add line’ on the toolbar, by default). Choose it, then hover the mouse over the ending or starting point of a line, and you'll see a plus symbol next to it—this allows you to continue the line. Similarly, it allows you to add a new point between other two by hovering the ...
Might be worth a thought:
If the undesired points are significantly(or just noticeably) higher than the rest of the data, you can convert to .txt, open in spreadsheet editor, sort z-value column by descending, manually remove all points higher than desired data height, and then convert back to .las