The composition of Silver tarnish is Silver sulfide, to quote from Wikipedia:
Silver sulfide is an inorganic compound with the formula $\ce{Ag2S}$. A dense black solid, it is the only sulfide of silver. It is useful as a photosensitizer in photography. It constitutes the tarnish that forms over time on silverware and other silver objects. Silver sulfide is insoluble in most solvents, but is degraded by strong acids.
The last sentence is important as Silver cleaning is not accomplished with harsh chemicals, but via electrochemistry which leads to the hydrogen atom radical formation, which then reduces the $\ce{Ag2S}$ liberating $\ce{Ag}$ and $\ce{H2S}$. Here is a short summary of likely mechanics:
$\ce{Al -> Al3+ + 3 e-}$
$\ce{H2O ⇌ H+ + OH-}$
$\ce{HCO3- ⇌ H+ + CO3(2-)}$
$\ce{H+ + e- ⇌ •H }$
Effectively, $\ce{•H}$ can operate as a $\ce{(e-, H+)}$ pair:
$\ce{Ag2S + 2 •H -> 2 Ag + H2S (g)}$
Here is a confirming source, which states to quote:
The nascent hydrogen may also act as a reducing agent as it evolves from the metal surface.
And also, per the same source, the formation reaction of Ag2S can be reversed:
In that case silver suffers attack by dissolved oxygen and present sulphide species according to Reaction (5):
$\ce{4Ag (s) + 2HS- (aq) + O2(g) ⇌ 2Ag2S (s) + 2 OH- }$ (5)
So working in air, it is advised to employ a base to drive the above equilibrium to the left. Also, in alkaline conditions expect the reaction:
$\ce{H2S + 2 OH- -> 2 H2O + S(s)}$
Which is also noted in the referenced source, to quote:
However, after the cleaning of heavily tarnished samples (immersed for 30 and 60 min) some small quantities of sulfur (~0.3wt.%) are detected on the surface by EDS analysis, and the colour is changed to light yellowish.
[EDIT] With particular reference to the thiourea system, it is described in this hydrometallurgy source. A cited reaction equation is:
$\ce{ Ag_2S + (SC(NH)(NH)2)2 + 2 H^+ + 4 SC(NH2)_2 -> 2 Ag(SC(NH2){_2}){_3}^{+} + S_o }$
Silver metal can then be recovered with reductive electrolysis.