Translation memories grow quickly with time and can get quite messy. If you want to do a bit of cleaning in your TM files, your options are limited. Some CAT tools, such as Trados Studio, allow you to work directly on Translation Memory files, but these interfaces tend to be heavy and not as user-friendly as you would like them to be.
Which software shall I use to edit TMX files, then?
My personal recommendation goes to Olifant, which is pretty easy to use: source on the left, target on the right. Editing is simple and you have access to powerful options to import/export files, search specific strings using advanced filters, etc. You can also easily split or join strings, modify the language codes for your TM and modify attributes.
In short, it lets you to pretty much anything with your TMX files, which you can them easily import back in your CAT tool.
The interface itself is quite light and reactive, which is a big advantage over Trados Studio’s TM Editor windows.
To top it all, Olifant is absolutely free! You have no excuse for not giving it a try.
If the interface of Olifant scares you a bit, you may give a try to another TMX editor that is now free: Heartsome TMX Editor 8. You can see a short introduction video, and you will find a lot of practical articles on the download link. Besides TMX editing features, Heartsome TXM Editor 8 offers a number of QA checking options (Target identical to source, numerical mismatch, etc.)
While I don’t have much experience using it, it should get the work done for your TM editing tasks, and may even serve as a free QA tool for your projects.
So which TMX editor should you be using? I think both software are pretty complementary. Olifant gives you some really powerful options to search strings, but regular expressions and the like can be tricky to apply well. Heartsome TXM Editor 8 is a bit more straightforward, and should do just what you want it to in most cases.
Since they’re both free, my best advice is to give them both a try, and then decide on which of them fits your needs best.