This will involve a massive change in the design, because (given the quantity of mountainous terrain) the text and house outline will be overwhelmed. The southern mountains stomp all over the text, and the strong curve formed by the valley conflicts with, well, everything you have there now.
In your shoes I would counsel against making that change, both because it makes a visually simple logo very complex and because it conflicts with the whole style of the logo (unless they sell mountain real estate, in which case you'll probably need to start over).
That said, in terms of expressing relief there are some approaches that could be made to work, although none of them is easy to do without looking kitschy. One is to break the background into half-tone dots and vary their shading and size where the mountainous areas are, using an actual relief map as a guide.
Another is to start with an image like the one below, selectively remove all the lowlands in Photoshop and run a something like a half-tone or pen sketch filter on it either in Photoshop or after importing to Illustrator. If you use a blend mode such as Luminosity on the layer and play with the Opacity, you may be able to transfer the suggestion of the mountains to the finished piece in a way that doesn't create too much mayhem.
A third might be to sketch in highly stylized mountains, very minimalist, in the same grey you're using for the text. This would be really hard to pull off without it looking like a cartoon-style tourist map.