The city of Durham which was where the Thompsons lived, had a population of about 70,000 in 1901 so it would have quite a few churches both Anglican and non-conformist not all of which will have deposited their records in the county record office. Most Anglican parish records will probably be deposited for this period - none are likely to be indexed and/or transcribed. Most indexes are for earlier periods.
The birth and probably the marriage took place in Lanchester registration district which at some point covered all these areas
Registration County : Durham.
Created : 1.4.1875 (previously part of Durham district).
Abolished : 1.7.1938 (succeeded by Durham Central, Durham Northern and Durham Western distrcts).
Sub-districts : Annfield Plain; Consett; Lanchester; Stanley; Tanfield.
GRO volumes : 10a (1875-1938).
Benfieldside, Billingside, Collierley, Consett, Conside & Knitsley, Cornsay ,Craghead, Ebchester, Esh, Greencroft, Greencroft Within, Healeyfield, Hedleyhope, Iveston, Knitsley, Kyo, Lanchester, Langley
Medomsley, Muggleswick, Oxhill, Satley, South Cornsay, South Moor, Stanley, Tanfield
So you would really need to know where they were living to know which parish records it might be best to try to search in the county record office for a possible baptism. You would need to employ a researcher to do the search for you.
This seems the most likely marriage
Marriages Jun 1906
CHARLTON Mary Elizabeth Lanchester 10a 615
Thompson Walter Lanchester 10a 615
Regards
Valda