The Winchester Model 61 was a very sleek designed .22 Ca. Hammer less pump Rifle which mfg. 1932-1963, at approx. 349,000 total Rifles in .22 cal. only.
Yet in the Short, Long, and Long Rifle Calibers. In 1960, and 1961 the .22 Magnum Caliber was Introduced. Less than 32,000 Magnum Caliber Rifles were produced at this Time.
Not classified as being Rare, but yet very desirable, in good shape among Collectors and Shooters alike. Referred to as the "WMR", Winchester Magnum Rimfire.
The Letter "A" will appear on the underside of the Receiver, on the Trigger Guard Assembly, and under the Serial Number, on the Magnum Cal. Rifles indicating an improved modification to the Breach Bolt! This First appearing around serial #324,000, and late 1960 of production.
As far as the Letter "B" under the Forearm, and I'm assuming that your talking on the Walnut Wood Forearm, which was Grooved, and in Three different types or styles.
There are no References anywhere indicating that Winchester Stamped a Letter "b' on their Wood stock, on the Model 61, that I am aware of.
As you state the Rifle doesn't appear to be Refinished, it is Possible someone has placed a letter B on the forearm showing ownership of their Rifle as this has happened in the past, especially where the wood is concerned as it's the easiest spot to do, and possibly fix if it doesn't come out right or needs to be removed. IMO!
Hope this Helps.