It depends on the carpet.
If old wool, leave in situ; worms love it.
If modern polyester etc, remove before building beds.
If unsure about it, cut a piece and see if it is tough there are nylon threads (modern), or if it is soft and starts to disintegrate (old wool).
PS 45cm is v high and 20cm of compost will give almost equal results, unless its a mobility question.
