@cccp64 Finally getting to this one 😉 
Note: I presume this used to work with other RMTV versions.
So the log already suggests that renaming and moving the file to the Trashcan failed (as you already knew).
A quick view at the sources (note that none of this has been modified in the last 5 years):
 
Renaming files is using whatever system function is defined per platform and how it comes with Lazarus Pascal.
So I think under Linux it uses the clib "rename" function (at least, this is what the Lazarus code suggests).
Not much I can do here without going overboard.
 
Moving things to the Trashcan is my own concoction, and this is what it does for Linux.
- RMTV tries to use "~/.local/share/Trash/" as the Trashcan location base directory.
- if that path doesn't exists it will try "~/Desktop/Trash/", "~/trash/", ~/Trash/", "~/.trash/", "~/.Trash/"
(all based on me not being a Linux expert, from whatever info I pulled from the Internet)
If "~/.local/share/Trash/" is used:
- "~/.local/share/Trash/info/" will be used for an info file (INI formatted), where the directory is created if needed and the info file gets the orignal filename plus the ".trashinfo" extension.
- "~/.local/share/Trash/files/" will be used to store the original file, where the directory is created if needed 
For the other trashcan paths these directories will not be created.
Next the original will be copied to the trashcan location and RMTV verifies if the copied file exists. If so, the original will be deleted.
* This since moving files may not work across network shares (not sure if that is 100% true or not, or if this may be a Lazarus limitation or not - its been a long time ago that I created the code for this and RMTV uses it ever since unmodified).
You are probably more experienced with access rights than I am, but could it be that your files may have different access rights than your usual files? I'm sure you already checked this.
Could it be that the Trashcan doesn't exist or is full? (just a random additional guess, but doubt it though in your case).
As I cannot reproduce this issue on my Linux Virtual Machine, I'm a little bit at a loss why its not working on your setup. Granted: I never use this option and so far it worked for those who do. Let me know what your findings are with the access rights.