Hi Julia,
It really depends on the quality of those backlinks. Let's use the Moz scoring system for this example. If you are losing 30 links with very low page authority (PA), low domain authority (DA), and high spam score, you will not be affected much, if at all. You shouldn't worry in this case. However, if you are losing 30 links with high PA, or high DA especially, you might be affected considerably, and should work to keep this links or get new links with similar PA and DA scores.