Thank you all for your comments and suggestions.
Here's the whole sampler, but as you can see, all of the work appears to have been done at the same time.
I can see the TSJSMS as being some sort of religious text or hymn or something of that sort, but SR, separated from the rest, puzzles me.
In 1841 Elizabeth was living with her widowed mother, Ann (her father died in 1839) and brothers at Debdon Burn Foot. There don't seem to be any family members whose names tally with those initials.
I was hoping there might have been standard acronyms used on samplers of the time, but realistically, the letters could mean anything or nothing. They just don't appear random. My Grandmother might have known the story behind it, but sadly I never paid much attention to the sampler until my mother inherited it, and now it is one of many unlikely-to-be-solved mysteries thrown up by my family history research.