Solution 1:

Shallow can be used as a transitive or intransitive verb (who knew!).

To be honest, I haven't heard it used very often (I would normally say that something was shallow, not that it shallowed), but it doesn't sound very strange to me either.

Solution 2:

For this context I suggest "lessen":

Putting the anvil on the mattress deepens the depression in it, but removing the anvil lessens it.

Solution 3:

Deepen has two meanings.

  • Deepen = Dig out

Antonym: Fill in

  • Deepen = intensify

Antonym: weaken

In the example above you can use the word mount or hollow out.

Solution 4:

for the example you've given,

removing the anvil lightens the depression?