Without additional restraining cords the familar bond degrades over the years. But what happens if the magus strengthends the bond as described in RAW?

I see two possibilities:

The bond is renewed, all Aging Points are reset.

The bond is strengthened as per the corerules, but the Aging Points remain, affecting the new bond strengths (either as distributed before or they redistribute based on the new strengths).

As for the cost of this process, there's also two possibilities:

Stick to the RAW and subtract the vis invested so far into bonding with the familiar from the new Lab Total.

Calculate a virtual lab total based on the current bond strength and use this as the basis for the current vis total of the bond. (This would seem excessive if used in conjunction with option #2 from above.)

Option 1 would offer a great alternative to the restraining cords, but would require the rebonding of the familiar every few years.

I'm pretty sure option 2 is what is intended. However, it should be noted that Aging Points themselves get erased once they've decreased a value according to the rules. So, for example, if you have a cord that has just decreased from +2 to +1, it no longer has any Aging Points so it is just like it had started at +1. So raising it from their is as though there are no Aging Points. However, as Tugdual replied, uncoupled systems are easier to deal with.

Erasing aging points affects the adversely affects the system though - if you intend on keeping tabs on how aging has affected a bond, you might as well go all the way.

Difference:
Cord 1, 2 AP (currently effective cord 0): New Lab Total +25 = 2 years at 3, then 3 years at 2,then 2 years at 1.
Cord 0: New Lab Total +25 = 3 years at 2, then 2 years at 1. (10 points have to be spent otherwise or are "wasted".)

The first variant puts a definite time limit on the bonds of faerie familiars, since it wouldn't allow you to keep buying up the cords from lower values - once a cord is at +5 it can't be raised further, and the accumulated Aging Points don't simply vanish. So a completely bond faerie familiar (lab total of 225 (!) for all cords at +5) would inevitably break free after 60 years (3 x 20 AP to reduce a cord from +5 to +0).

The second variant allows you to extend the bond indefinitely as long as you manage to increase your lab total by 5 points every two years in order to buy a cord from +0 back to +1.