What is the Attributable Risk of birth defects in Zika infected pregnancies?
The article cited in the question (Vital Signs: Update on Zika Virus–Associated Birth Defects and Evaluation of All U.S. Infants with Congenital Zika Virus Exposure — U.S. Zika Pregnancy Registry, 2016) gives the base rate for the definition of "birth defect" that they use:


  The baseline prevalence of defects consistent with those that have been observed with congenital Zika virus infection was approximately 2.9 per 1,000 live births in the pre-Zika years (4). The initial findings from the USZPR represent an approximate twentyfold increase in Zika virus–associated birth defects among pregnant women with laboratory evidence of possible recent Zika virus infection, with an approximate thirtyfold increase in brain abnormalities and/or microcephaly. 


The reference for that background is Baseline Prevalence of Birth Defects Associated with Congenital Zika Virus Infection - Massachusetts, North Carolina, and Atlanta, Georgia, 2013-2014.:


  These data, from Massachusetts (2013), North Carolina (2013), and Atlanta, Georgia (2013–2014), included 747 infants and fetuses with one or more of the birth defects meeting the case definition (pre-Zika prevalence = 2.86 per 1,000 live births). Brain abnormalities or microcephaly were the most frequently recorded (1.50 per 1,000), followed by neural tube defects and other early brain malformations† (0.88), eye abnormalities without mention of a brain abnormality (0.31), and other consequences of central nervous system (CNS) dysfunction without mention of brain or eye abnormalities (0.17). During January 15–September 22, 2016, the U.S. Zika Pregnancy Registry (USZPR) reported 26 infants and fetuses with these same defects among 442 completed pregnancies (58.8 per 1,000) born to mothers with laboratory evidence of possible Zika virus infection during pregnancy (2). Although the ascertainment methods differed, this finding was approximately 20 times higher than the proportion of one or more of the same birth defects among pregnancies during the pre-Zika years.




According to Estimating the Number of Pregnant Women Infected With Zika Virus and Expected Infants With Microcephaly Following the Zika Virus Outbreak in Puerto Rico, 2016. the background of microcephaly in Puerto Rico was around 12 cases per year, while they estimated 180 cases would occur in the presence of Zika. 


  We estimated an IQR of 5900 to 10 300 pregnant women (median, 7800) might be infected during the initial ZIKV outbreak in Puerto Rico. Of these, an IQR of 100 to 270 infants (median, 180) may be born with microcephaly due to congenital ZIKV infection from mid-2016 to mid-2017. In the absence of a ZIKV outbreak, an IQR of 9 to 16 cases (median, 12) of congenital microcephaly are expected in Puerto Rico per year.


This is modeling, not pure observation, but was based on observed risk. The paper is online full-text (I think) so you can follow through the assumptions if you want.