Although both $\frac{of ~them}{\left(A\right)}$ $\frac{are\ trying}{\left(B\right)}$ $\frac{to\ get}{\left(C\right)}$ the scholarship she has the $\frac{highest}{\left(D\right)}$ grades

The correct sentence is:

Although both of them have high grades, the scholarship is given to the highest grades.

Here's a breakdown of the errors in the other options:

• Option 1: "Although both the scholarship she has the high grades" is incorrect because it lacks a clear subject and verb for the first clause.

• Option 2: "Although both of them have high grades, the scholarship she has the highest grades" is incorrect because it uses "she" instead of "they" to refer to both people.

• Option 3: "Although both of them have high grades, the scholarship is given to the highest grades" is correct.

• Option 4: "Although both of them have high grades, the scholarship is given to the highest" is incorrect because it lacks the word "grades" after "highest."

Therefore, option 3 is the correct sentence.