To find the sum of all two-digit numbers that give a remainder of 3 when divided by 7, we need to identify all the two-digit numbers that satisfy this condition and then add them up.

Finding the two-digit numbers:
To find the two-digit numbers that give a remainder of 3 when divided by 7, we can start by listing the numbers from 10 to 99 and checking if each number satisfies the condition. However, this method can be time-consuming.

A more efficient approach is to observe the pattern of remainders when dividing numbers by 7. The remainders repeat after every 7 numbers. The remainders for the numbers 10 to 16 are 3, 4, 5, 6, 0, 1, 2. From this pattern, we can see that the numbers that give a remainder of 3 when divided by 7 are 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, 80, 87, and 94.

Summing the two-digit numbers:
To find the sum of these numbers, we can employ the formula for the sum of an arithmetic series. The formula is Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, the first term is 10, the last term is 94, and the number of terms is 13.

Using the formula, we can calculate the sum as follows:
Sn = (13/2)(10 + 94)
= (13/2)(104)
= 13 * 52
= 676

Therefore, the sum of all two-digit numbers that give a remainder of 3 when divided by 7 is 676.

In conclusion, the correct answer is option 'B' (676).