Teamviewer and Linkmein/logmein (and others) are not scams in themselves - these are legitimate file sharing websites where one pc user can link up with another and open up the whole of the pc's contents to share. This is done by using one of these websites to download a piece of software - a program - to open up your pc's contents so the other person can borrow/see/use anything that they need.
If done between trusting friends this is not a problem and can be a useful tool - but there are many unscrupulous organisations/individuals out there that trick you into using these websites's software downloads to gain remote access to your pc - they work under the guise of 'repairing or cleaning up' your pc but in fact they are corrupting it by deleting system files and planting mal-ware or spyware to permanently scrutinise anything you do on your pc - including financial transactions. They will then charge a premium to "clean up" your machine and then convince you that you need to have them protect your pc from viruses and errors remotely - again paying them a fee (monthly debit) to do this.
This is the scam - a good anti - virus/ internet security software is all you need plus an occasional "defrag" and "drive clean" which can easily be done by going into "accessories" then "system tools" and clicking on "disk clean up" or "disk defragment" and away you go.
One of these "file - sharing" websites did have a warning in red on their site a while ago which warned that if anyone asks you to download their software program on the pretence of cleaning up your pc that this is a scam. Particularly if it is a cold-caller with an Indian accent, even if they say they are from Microsoft or have been advised by them.
So basically, these file sharing webs are fine and very useful - they are designed for music or file sharing between legitimate people or for helping friends sort out pc problems. If you allow a total stranger either from someone phoning you up (or as Lenarda did - using a PC maintenance company that she found online) remote access to your pc using the file sharing websites' software you are exposing everything that you have on your hard drive - all your history and every transaction.
Look up "India computer scam" and you will find a wealth of information.
Krys UK (Dobrzanska - researching Starzak, Gierula, Khlyuchanka lumber camp - Perm)