Hi,
I think the standard line is that any links like this should be branded only and no followed if you want to be as safe as possible. If an option it has been suggested to try having them only on a homepage or on a partners type page rather than a sitewide link in the footer for example. As to if they should even be there at all, well I guess this depends if they were created purely for the link or if they bring in some marketing value from referrals/brand recognition.
Assuming you have been affected by Penguin then I wouldnt think that reducing the keyword usage on the homepage will help much. You will need to monitor carefully since #4 ranking is still visible and if you start adjusting multiple onpage and offpage variables at the same time you could all of a sudden be looking at a bigger drop and be stuck wondering which of the changes might have contributed to this! Even messing with the existing backlinks could cause further fluctuations so it sounds like a fine line you are on now. I would try making small changes and monitor for a week or two before proceeding with other edits.
