Remove 2 GFCI breakers and install a tandem if the box accepts a tandem

It sounds like you may be mistaken as to how this is wired, or that perhaps I'm just not understanding your explanation. As others have mentioned, it's not possible to get 240 volts from a single pole in a 120/240V split phase system. Each tandem breaker provides 2 120 V circuits, this is true. However, if you measure between the terminals on a single tandem breaker, you'll get 0 volts. This is because the terminals are both powered from the same leg, and so are at the same voltage potential. If you measure from a terminal on the top tandem breaker to a terminal on the bottom one, then you'll measure 240 volts. This is because each breaker is connected to a different leg, which are each one half of a 240 volt circuit.

With all that said. For this setup to work, one appliance would have to be connected to both breaker. Something like this...

Notice that each appliance circuit has one wire connected to each of the tandem breakers. In this situation, you'd need a device like Speedy Petey shows.

Which ties the breaker handles together, to provide common trip characteristics.

Notice how the inner handles are tied together, and that the outer handles are also tied to each other. This way if either trip (or are turned off by the user), the entire circuit is shut off.

If this is wired the way you've explained, where the dryer is connected to the top tandem and the heater is connected to the bottom. Then there's some magic going on in those breakers.

You'll need a double-pole GFCI breaker, wired like so:

What you have described is a multiwire branch circuit. Because the neutral is shared, the overcurrent protection device(s) (in your case the two separate breakers) must be able to trip together.

This can be remedied by installing a double-pole breaker, or by handle-tying two individual breakers. However, since you already have a need for GFCI protection, go ahead and install a double pole GFCI breaker.

However, existing lights might not need GFCI protection if they are 5 ft or more away from the pool (horizontally) and 5 ft or more above the maximum water level of the pool. Within 5 ft and below 5 ft above the maximum water level is not allowed. See (B)(3) and (4).

If you move or install new lights, they are subject to new installation requirements. See (B)(1).

2014 NEC

680.22 Lighting, Receptacles, and Equipment.

(B) Luminaires, Lighting Outlets, and Ceiling-Suspended (Paddle) Fans.

(1) New Outdoor Installation Clearances. In outdoor pool areas, luminaires, lighting outlets, and ceiling-suspended (paddle) fans installed above the pool or the area extending 1.5 m (5 ft) horizontally from the inside walls of the pool shall be installed at a height not less than 3.7 m (12 ft) above the maximum water level of the pool.

(3) Existing Installations. Existing luminaires and lighting outlets located less than 1.5 m (5 ft) measured horizontally from the inside walls of a pool shall be not less than 1.5 m (5 ft) above the surface of the maximum water level, shall be rigidly attached to the existing structure, and shall be protected by a ground-fault circuit interrupter.

(4) GFCI Protection in Adjacent Areas. Luminaries, lighting outlets, and ceiling -suspended (paddle) fans installed in the area extending between 1.5 m (5 ft) and 3.0 m (10 ft) horizontally from the inside walls of a pool shall be protected by a ground-fault circuit interrupter unless installed not less than 1.5 m (5 ft) above the maximum water level and rigidly attached to the structure adjacent to or enclosing the pool.