No big deal. Your choice: Leave them or remove them.

Fungi are an important part of the soil ecosystem and will help begin the break down of organic matter, especially woody material, so bacteria and other microbes can finish the job. They are generally not harmful to the garden.

If that "compost" is growing mushrooms then it was not composted enough and is not really compost.

If that "compost" is growing mushrooms then it was not composted enough and is not really compost.

That's nonsense!! Any decomposing organic matter - such as compost - can develop mushrooms. Mushrooms are only the fruiting bodies of various fungal organisms and fungi are certainly active in compost at pretty much any stage of the composting process. That's what that often sheet-like, white substance is underneath a layer of compost or mulch - mycelia or fungal filaments.

To get compost as fully decomposed as it needs to be to NOT generate mushrooms or develop mycelia takes a good long time - often many years - and it is then referred to as 'humus'.