I don’t see a problem with this. If the person is praying for others, invoking the help of the Holy Spirit, it is possible he/she has been given the gift of healing, which is always meant to be used for the Body of Christ. This gift is not necessarily given only to Catholics. God’s gifts are not limited to a particular faith, but if the person is baptized, he has gift of the Holy Spirit, Who empowers him to minister healing. Sometimes it may just be the community offering prayers for the sick, which is pleasing to God as they pray together for one another.
Bear in mind that this type of service is not to be confused with our sacrament of Extreme Unction, the Sacrament of the Sick as it is often called.
During Lent our local churches hold ecumenical services at one another’s churches. These are well attended by the various faiths. True, it is not a healing service, but the only difference in a healing service is that this gift is ministered through a prayer offered for the health of those in need.