I don't know the details of the ERS system in New York State but can provide some points to watch out for when deciding whether to take that money out of ERS or to leave it there.
You say that your wife contributed $4K+ to her retirement.
Does ERS credit interest on this sum (often as a lump sum annually) on the total amount in her retirement account? If so, what is the annual rate (this is often guaranteed in the retirement system contract)? Can your wife do better than this rate after withdrawing the money and investing it elsewhere? Note that this interest is different from any employer contributions to the State retirement plan. Employer contributions by the State into its own retirement plans cannot be withdrawn by the employee at all; they serve only to determine the monthly pension payment amount your wife will receive when she reaches retirement age.
Were your wife's contributions to ERS pre-tax or post-tax? If the former, she will likely owe income tax (both State and Federal) on the amount withdrawn, while if the latter, she will owe income tax only on the interest credited by ERS. None of these tax considerations will apply if the withdrawal is rolled over (preferably as a trustee-to-trustee transfer) into an IRA.
Next, did the annual interest payments cease when your wife left her teaching job? If so, there is little reason to keep the money in ERS.
Finally, will ERS re-compute her interest payments if she takes a lump-sum payout instead of just letting the money ride till she reaches retirement age and taking a pension then? For example, my state retirement plan credited 8% interest annually but if I had chosen to take a lump-sum payout even at retirement, the interest would have been recomputed as if it had been 4.5% all along and the payout reduced considerably from the account value as shown in the most recent statement of account from my retirement system.
Given the relatively small value of your wife's retirement account, you might decide that it is best to just take the money and run, but since you say "Is there any reason why I shouldn't just pull what she has contributed?" (emphasis added), be aware that even if you handle all financial matters for the family, you have no right to pull out what your wife has in her retirement account; she has to make the decision and sign the paperwork.