I'm not sure the painting is significant, or if it's the restaurant itself that is significant.
The restaurant shown is the Rules Restaurant, the oldest restaurant in London. The painting shown in Spectre does indeed hang there and doesn't appear to be a particularly famous work.
Therefore, I'd suggest the restaurant symbolises a few things:
Firstly, M - like Bond - enjoys the finer things in life, including being at an old and well-respect restaurant. This would fit with his character from the novels, who enjoyed frequenting The Blades Club.
Secondly - and perhaps more symbolically - it could symbolise a meeting "of the old". The plot of Spectre follows Max Denbigh, as an agent of Blofeld, introducing the Nine Eyes spy system. Denbigh dislikes the 00 unit and wants to impose total surveillance on the state, under the guise of protecting the people.
He comments on a number of occasions to M about how irrelevant he believes him and his unit to be in the modern world:
Denbigh: When are you going to realize you don't matter anymore?
not. But something has to.
On another occasion, Denbigh also comments:
Denbigh: Take a look at the world... chaos... because people like you,
paper-pushers and politicians, are too spineless to do what needs to
be done so I made an alliance to put the power where it should be, and
now you want to throw it away for the sake of democracy, whatever the
hell that is. How predictably moronic.
Therefore, I like to think the meeting in the restaurant symbolises a meeting of "the old". M and his unit are viewed to be outdated and unnecessary in the face of modern surveillance. They meet in the oldest restaurant in London and M tells his unit they cannot interfere - they cannot help any more, they have no power.
Obviously as the film goes on, they do interfere and they do help Bond. But at the time of the meeting, the old restaurant symbolises the lack of power of M and his unit perfectly.