Part of the cost-saving process for creating an msr was to leave out the 3rd repro-only head. What you have is an erase head on the left and a record/symc-repro head next to it. 3rd repro heads are primarily convenient for alignment purposes and in the real old days, were necessary for repro as sync/record heads were pretty terrible in frequency response.
To a certain extent, the strength of bias current used for an erase head function can be adjusted on most machines.....if you have test equipment and learn the procedure based on your msr service manual. Your msr owners manual might actually have a chapter on adjusting this internal parameter.
Of course the msr might not have this adjustment...or if it does, it still might not clear your problem because any number of things can make an erase head "not erase fully". Including the condition of the head. You could take the machine to a tech and have them adjust it.
Or, better yet, you could send it to Montebello (if you're in the U.S). At least there, if the machine needs a new head, they can replace it with a factory piece...and perhaps do the same if your record/sync head is also getting to the end of it's life. We're getting to the end of days where these heads are going to be available at Montebello...and adjustments/relapping only work for so long. However...head replacement at Montebello is not cheap for most machines. You have to weigh all this against what you paid for the machine and how many years from now it can be adjusted and kept useable for you to record on.
Now having said that, you could just ignore the problem. Especially if the level of residue isn't so loud that it creeps into newly recorded tracks. A bulk eraser would certainly clear out all signals when you need a clean reel. And be a comparatively effective band-aid solution at low cost. Just make sure you get a bulk eraser designed for half-inch tape or larger. If you only get one designed for quarter inch tape (or worse yet, a hand-held model) you won't be achieving a full erase.