try cleaning the old grease off the part, underside also.. use some WD-40 to spray on it and the old grease will loosens up... then work it back an forth a few times and you are ready to go...you might then want to put some new lithium grease( white grease) on it to keep it moving...
rememberr WD-40 is not a lubricant, it cuts grease, will thin it do you are really using the old grease again... its the dirt that the grease picks up that is causing the part not to move like it did when new.... clean off the dirt with some rubbing alcohol and relube.