It is true that the scriptures encourage us to make a joyful noise unto the Lord. That doesn't mean it has to be something that is hard for the congregation to listen to. As the worship leader, it is your job to coordinate that joyful noise. Look, it is not a sin to point out to the offending members of the praise team that they are singing off-key. Perhaps they don't even know it. A couple of suggestions:
It is very likely that they are not even aware that they are not singing on key. As a subtle way to point this out to them, record the praise team performance, or a rehearsal and get the members together to view/listen to it to critique it. Even let the off-key singers do solos so that it is clearer as to what is really going on. Perhaps this will be enough to get them to either bow out, or work on improving their range.
Singing off-key is something that can be corrected with a coach. Why not seek out a coach for this purpose? Sometimes it is simply a matter of making better choices as to what and where they can best contribute. Find their range and build your arrangements around what they can sing.
Some churches have multiple praise teams that alternate weeks. If your church already does this, then split the poorer singers onto each of the teams to lessen their effect. If your church doesn't do this, suggest it as a means of getting more talent involved, and make sure you are involved in the auditions.
Either way, you are not in the wrong to point out that the members of your praise team are not living up to the minimum requirements of the job. There are many ways of worshipping God on Sundays. Perhaps theirs is taking care of infants in the nursery (something there is always a need for)