Finding all marked elements using Grover's algorithm

As part of an assignment I am supposed to design a variant of Grover's algorithm that finds all $t$ marked elements. I guess like most people I'm more familiar with classic computation, so the solution that I came up with is simply to repeat the following procedure $t$ times, similar to the solution here:

1. Use Grover's algorithm to find any marked element $x$.
2. Delete $x$ from the data base.

My problem is that I am unsure to how the deletion operation can be realized the easiest. Can anyone recommend a 'standard way' of doing this (assuming there is one)?

Thanks!

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