Hi
I have looked for a marriage on Scotlandpeople and cannot find one for the time period, I have looked under the surnames only, between 1900 - 1922, as Jessie may be a pet name, with no results.
I have also looked at the 1911 census for Jessie, there are 4 possible for Lanark, but she may not have been born there.
I am not sure where to go from here, hopefully there may be someone on here, that has more knowledge on the Scottish records than me, that may be able to help further.
Margp