First my disclaimer that i am only answering because no one else has done so. I am not an H&K expert and rather far from one actually. First, here is a website that i located that may be useful for some basic information: http://world.guns.ru/civil/de/heckle...-6-sl-7-e.html
I have owned H&K SL7 and SL6 rifles. The former parallels the H&K 770 in chambering the 308 Winchester cartridge. (The latter chamber the 223 round.) I have only fired them for function and that they did well. I offer the following thoughts just as starting points for your further inquiry if you wish to pursue the matter. The 770 was derived from the paramilitary SL7 design. It was one that was in turn designed for a specific military market. I have heard conflicting stories as to whether any of these weapons were ever sold or delivered in either chambering. Apparently in any case, they became available on the American market. The chambers of these weapons are fluted to assist extraction. The only practical consequence is that the brass is sufficiently deformed so that it cannot be reloaded. These seem to me best described as 'period rifles', representing an era (the nineteen eighties) but semi auto design has moved on. They were expensive then. Relatively well made but offering no more real reliability or material features (except the availability of a ten round magazine) than other more value competitive domestic rifles. There were also the normal issues of warranty and parts availability that is always a concern regarding foreign products with limited distribution channels. Such is even of greater concern today particularly if the rifle is to be employed in the field. But essentially, they just did not offer anything to the market to justify their price. I believe that the military models do continue to appeal to a certain American market segment, but the 770 sporting model lacks even this appeal base. Perhaps these are 'collectible' today, but I believe that may be more in the minds of the owners trying to purvey them. In summary, a good but highly overpriced rifle with really little to recommend it over other contemporary new/used rifles such as Remington or Browning models. Also, the latter are offered in a variety of chamberings. As to you description of the specific weapon in issue. Two remarks. First, the scope rings do add some value. My information is too outdated to estimate a price for the rings. Second, the "good condition" would be a big caveat to me. I would want such a rifle in at least excellent condition. This would not be a rifle that I would want to buy into a repair of any sort. I would pass quickly unless the rifle was bargain priced and I could clearly ascertain the actual condition. Of course, if you are 'in love' with it, I can understand that. Then just shop carefully and with patience.
Just my take.