I love a good mystery and attempted to search the web for icfinst.exe and Icfinst.exe.mdmp using hundreds of search engines hoping to get a hint at what this executible might be. Except for a couple other search request for the same info by others from this tech site, no luck.
Make sure you have all files and folder options In 'My Computer,Tools, Folder Options, View... set to reveal all files to include system and hidden files and repeat your search for this file... if found, see if you can identify it by its' properties, If found and no info given.... try running it by double clicking on it... it sounds like it might be an installation file of some sort and most of those will have options to cancel out or uninstall if necessary... but, hopefully it will give some clue as to what it belongs to.
If file is still not found... I would agree with wparsons suggestion, with 2 caveats 1.to backing up the registry first. Additionally I would type services.msc from START,RUN and export the listing and save it. After which I'd delete both entries... and restart.... rerun services.msc and compare listings before and after to see if important stuff has stopped working... If so, or if obvious errors at restart, Restore Registry as required. However, if still no problems noticed, you probably won't miss those entries until you run some very unique software on your system... I.e. some old Dos software file, or such. Most likely, this item is just a leftover entry from some program you've removed long ago. I know I'd delete it in a minute... but like to err on the side of caution with a backup....