How cold does it get in the winter where you live? Venting a dryer to the garage (especially in winter) means that you're pumping humid air into a cold place . . . which almost guarantees condensation and mold.
Another concern is the passing of fumes (from say, a car running) in the garage back into the home through the vent opening. Personally, for only 200$ I'd get it done properly.
+1, mold is bad. Wet wood also rots, which leads to structural problems eventually. Get that humid air entirely outside the building envelope, especially if you are in an already humid climate.
The risk of fumes from cars, etc. entering depends on whether your house has a positive pressure relative to the outside, or negative pressure. Negative pressure is created by pumping air inside your house to the outside via running a kitchen range hood, bathroom exhaust, or warm air rising up your chimney (all very common). Positive pressure is created by forcing air in from outside, which is usually done by ventilating equipment such as heat recovery ventilator (HRV), energy recovery ventilator (ERV) or ventilating dehumidifier, none of which are common in a home built in 1968. Those are installed to prevent or address indoor air quality issues, and while they work well, are expensive to install and maintain. They are only really necessary if you are correcting a problem (radon gas is a good example) or have done a deep energy retrofit, air-sealing the house to such an extent that you need to bring in fresh air constantly. All that to say that you probably have a negative pressure, and could theoretically pull fumes into your house via the dryer vent. Probably not enough to notice, but why allow that stuff in at all?
My last place had the dryer vent into the storage room that had large openings to the outside; temperature/humidity were not a problem but after a year or two I got fed up with everything being covered in lint and added an extension to exhaust to the outside. Dont remember but I think materials were under 30$, just needed a dril, jigsaw, some screws and zipties. Really was not hard at all. Without knowing your specifics its hard to be sure but dryer vent lines are not hard for a do-it-your-selfer. But even hiring it out for 200$ I would have it done.
+1, this should be well under $200 if you DIY.