I have a network of many connected lines where there is overshoot topological errors. Is there any way to remove them using FME Desktop?
For FME2018 I would strongly recommend the Intersector transformer. It has a new tolerance parameter and it can quite easily clean up a lot of issues like this.
But it also partially depends on what you are going to do with the data afterwards. Most techniques will split the line at the intersection, leaving the overshoot as a small piece of linework.
If you are building polygons, then it's easy to ignore the overshoots (they appear out of the unused port). Otherwise you could apply a LengthCalculator transformer and simply remove lines less than x length (maybe 0.5 metres or however big the overshoots are).
The Snapper transformer is useful in this scenario
"Brings lines, segments, end points or vertex points of features together if they are within a certain distance of each other and (optionally) if they have one or more attributes in common.
The difference between the AnchoredSnapper and the Snapper is that anchor features are considered to be accurate and consequently do not move."
But consider using a combination of transformers to to improve your chances of removing under and over-shoots.
Note there is a module called MRF2DCleaner http://docs.safe.com/fme/2018.0/html/FME_Desktop_Documentation/FME_Transformers/Transformers/mrf2dcleaner.htm?Highlight=mrfc%20cleaner but this is at additional cost and only on the 32 bit version of FME. Contact the vendor for a cost.