The fact of the matter is that you used the 11th attribute in the study, and so to re-estimate the model by ignoring the 11th attribute would be to lose information and add more noise to the utility estimates.

If we can assume that the utility estimates for the 10 items are essentially independent of an 11th item that might be added to the experiment, then the simple approach is to estimate all 11 utilities as you have done, but then just to omit the 11th item in the reporting (and rescale the other 10 utilities assuming only 10 items were included in the experiment). The software documentation on MaxDiff utility estimation gives more detail about how to rescale the utilities under the different approach (raw utilities, probability scores summing to 100). You can rescale the 10 utilities (omitting the 11th) in a program like Excel once you know those formulas.