That's up to you but there is no real reason to remove them if the plants are growing well sine they were transplanted. Most don't recommend transplanting plants with fruit on them. If there are some they remove them. But some do leave them on with no problems.

On the other hand "the plants don't look well" can mean many things and it may have nothing to do with the fruit on them. Can you post a picture or at least provide more detailed description? The name of the variety and the size of the plant would help too.

It takes an average of 6 weeks for fruit to ripen so one month is too soon to expect ripening.

So basically removing them is your choice if you feel it might help. The worst that can happen is you'll have to wait even longer for ripe fruit.

Dave